# Quantum Mechanics Questions And Answers Pdf

AN INTRODUCTORY GUIDE Format : PDF - Updated on December 19 INTRODUCTORY QUANTUM MECHANICS LIBOFF SOLUTION MANUAL. many uncertainties and unanswered-questions. Beckwith1 1) abeckwith@uh. If you lost points on this question, please bring your exam to Professor Cramer and your score will be adjusted upwards 6 points (i. what are its independent variables and how many are there)? 6. Mark the best answer A, B, C, D or E on the Answer Sheet. Angular Momentum in Quantum Mechanics 4. Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. Click on the link to see the pdf with the question. These are the books for those you who looking for to read the Advanced Quantum Mechanics Materials And Photons Graduate Texts In Physics, try to read or download Pdf/ePub books and some of authors may have disable the live reading. com/2017/11/quantum-physics-hc. Cohen-Tannoudji won the Nobel Prize in Physics in 1997. State the four quantum numbers, then explain the possible values they may have and what they actually represent. This corrected second edition contains new material which includes solvent effects, the treatment of singlet diradicals, and the fundamentals of computaional chemistry. Although the Hamiltonian method generally has no advantage over (and in fact is invariably much more cumbersome than) the Lagrangian method when it comes to standard mechanics problems involving a small number of particles, its superiority. Introductory Quantum Mechanics Liboff Solutions Manual Pdf >>>CLICK HERE<<< Version 9. On the contrary, the quantum mechanical photon is ill defined regarding its position and time. 3,2,2 Double dumbbell or dumbell and donut See text. 1 Wave packets Waves can be long with many vibrations, as when you hum, or they can be short, as in a shout. 2015: Classical Mechanics 2015 Question Paper DU Msc Physics. Th eir answers will help us discover the limits that quantum mechanics imposes on our world and understand the range of possibilities that are allowed, including the role of quantum mechanics in nature. How to download the H. This way of using quantum mechanics. Single Photon Interference You should answer two sets of questions: (1) before your first laboratory session and As dictated by quantum mechanics. Finite square well 4. The Avengers Movie Free Download Hd. Entanglement is one of the most mysterious aspects of quantum mechanics and is ultimately the source of the power of quantum computation. The problems are from Chapter 5 Quantum Mechanics in One Dimension of the course text Modern Physics by Raymond A. What is the de Broglie wavelength for an electron moving at 2. This chapter is devoted to several attempts at showing the necessity of quantum mechanics. That’s the purpose of Quantum Mechanics. Unlike other compilation of exercises for qualifiers (such as Princeton or Chicago Problems, or the one mentioned below), they make no excuse for economy and include as many problems from all levels for each subtopic. notably those of quantum equilibrium and of the eﬀective wave function of a subsystem. correctness of quantum mechanics? We describe the con-struction of a speciﬁc kind of quantum random number generator for which the answer to these questions is af-ﬁrmative. Problem 1). Mathematical physics pdf and ebooks 1. Qualitative Questions: 1. Downloadable Solution Manual for Modern Quantum Mechanics, 2/E, J. However, most of them find it difficult and can’t complete physics hw without some professional help. We ﬁnd that a Bohmian universe, though deterministic, evolves in such a manner that an appearance of randomness emerges, with empirical distributions in agreement with the predictions of the quantum formalism. I show how a conception of subjective probabilities as degrees of care (inspired by Hilary Greaves) would answer the first question; and how interpreting quantum weights as proportions of worlds would answer the second question and help answering the third one. b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of the wavelength. , quantum dots) • Required to understand chemistry. For multiple-choice questions, the correct answer is provided. RE: Quantum hacking questions for a sci-fi project By PESchoenberg - on August 18, 2019 So far, no one has shown experimentally that it is possible to eavesdrop a quantum system without disturbing it. At the top of the applet you will see a graph of the potential, along with horizontal lines showing the energy levels. Quantum Mechanics Bransden 2nd Edition More references related to quantum mechanics bransden 2nd edition Physics Objectives And Theory Question Answer 2014. Use the links below to download past papers and model answers. Now lets apply this concept to the world of quantum mechanics. Rotational Motion in Classical Physics 3. Use the results of the previous two questions to show that the hamiltonian, H, one of the developers of quantum mechanics, Hermiticity and its consequences 5. If you have questions about quantum physics but have been looking for a book that will actually explain the subject, than look no farther. 3 QUANTUM CHEMISTRY • In principle, solve Schrödinger Equation • Not possible for many-electron atoms or molecules due to many-body problem • Requires two levels of approximation. Light is commonly described in terms of brightness and colour. 2,1,1 Dumbbell See text. ADVANCED QUANTUM PHYSICS. quantum state of the apparatus must take into account the interactions with the environment in some statistical way. Scribd is the world's largest social reading and publishing site. 2 "It from Bit" as Guide in Search for Link Connecting Physics, Quantum and Information In default of a tentative idea or working hypothesis, these questions, no's and clues — yet to be discussed — do not move us ahead. - Neils Bohr We typically view quantum mechanics as applying to the fundamental particles or fields of Units 1 and 2—not to the objects we find in a grocery store or in our homes. 2013: Quantum Mechanics-I 2013 Sem I DU Msc Physics. Because the smallest allowed value of the quantum number n for a simple harmonic oscillator is 0. correctness of quantum mechanics? We describe the con-struction of a speciﬁc kind of quantum random number generator for which the answer to these questions is af-ﬁrmative. The article looks at the possible role of measurement in a quantum-mechanical description of physical reality. IS QUANTUM MECHANICS INVOLVED AT THE START OF COSMOLOGICAL EVOLUTION? DOES A MACHIAN RELATIONSHIP BETWEEN GRAVITONS AND GRAVITINOS ANSWER THIS QUESTION? Andrew Beckwith Chongqing University Department of Physics; e-mail: abeckwith@uh. This is the solution manual for Riazuddin's and Fayyazuddin's Quantum Mechanics (2nd edition). Th eir answers will help us discover the limits that quantum mechanics imposes on our world and understand the range of possibilities that are allowed, including the role of quantum mechanics in nature. • Your score will be determined by the number of questions you answer correctly. However, most of them find it difficult and can’t complete physics hw without some professional help. Does Entanglement Disprove The Principle of Locality? Short answer: Yes. Classical mechanics predicts that the radiant energy produced by oscillating objects is continuous. Yes, within the constraints of the uncertainty principle. Feynman Quantum mechanics and path integrals pdf Feynman Quantum mechanics and path integrals pdf : Pages 384 By Richard P. Special theory of relativity was combined with quantum mechanics to produce a new branch of physics called 'relativistic quantum mechanics'. We'll discuss this further in the chapter on quantum mechanics. rights research papers problem solving interview questions and answers essay writing tutor jobs in ny state farm agent. CHEMISTRY 461 FINAL EXAMINATION JUNE 18 2001 This examination consists of 40 multiple choice questions. com later. To get started finding quantum mechanics mcintyre solutions download, And you are right to find the biggest collection of listed. Quantum chemistry is hard, so it is very useful to have this book!I only rented this book because I. The wave function for n electrons: MANY ELECTRON WAVE FUNCTION. Each week's notes come with a blog entry where you can ask questions and make comments. Which of the following isn’t a truth about quantum mechanics? A. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. And finally it stops responding if you ask it too many questions: incompatible observables. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. Advanced Quantum Mechanics Fall, 2013 Building on Professor Susskind’s previous Continuing Studies courses on quantum mechanics, this course will explore the various types of quantum systems that occur in nature, from harmonic oscillators to atoms and molecules, photons, and quantum fields. Fully solved examples with detailed answer description, explanation are given and it would be easy to understand. Here I'll give two answers to the question: Why quantum eld theory? Answer 1: Because the combination of quantum mechanics and special relativity implies that particle number is not conserved. 1 Bound problems 4. “If you observe an entangled quantum particle ” says Alice, “you get an answer,” says Betty. Select the best answer from. Quantum mechanics solved problems pdf. Dželalija, Physics Mechanics Physics is concerned with the basic principles of the Universe is one of the foundations on which the other sciences are based is tipical experimental science The beauty of physics lies in the simplicity of its fundamental theories The theories are usually expressed in mathematical form Mechanics. Choose your answers to the questions and click 'Next' to see the next set of questions. However, it is answer (b) that is correct. 3 nm, what is the energy and frequency of a photon of this light? Note: Planck's constant = 6. Quantum Mechanics Practice Test. Who are the founding fathers of Quantum Mechanics? Werner Karl Heisenberg Isaac Newton Erwin Schrodinger A and C. 109 x 10 31 kg 3. Get to the point GATE (Graduate Aptitude Test in Engineering) Physics questions for your exams. Other books that I recommend include A Modern Approach to Quantum Mechanics by John S. Lets look at the simplest case of electron motion: 1 dimension, or a straight line. differential equations notes by men prakash sahu3. So to summarize: Quantum Mechanics doesn’t give any definitive answers; it deals in probabilities. This science article is a stub. Planck’s Constant and the Speed of Light. Contact experts in Quantum Physics to get answers | Solutions to scientific and research problems, and discussions about Quantum Physics Explore the latest questions and answers in Quantum. Unlike static PDF Quantum Physics solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. Our online quantum physics trivia quizzes can be adapted to suit your requirements for taking some of the top quantum physics quizzes. Quantum Mechanics: The Theoretical Minimum by Leonard Susskind and Art Friedman (note, there are other 'theoretical minimum' books) This book is priced like a novel (at least the penguin paperback version is) and, at least in Europe, seems to be widely available in book stores. Moyer, Saunders College Publishing, 2nd ed. Book Description: Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, publishedMathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Two more quantum numberscharacterize states within the subshells. Very helpful. Quantum mechanics is the field of physical science that deals with the. A radical new theory plays into that, proposing that parallel universes exist and interact with each other ‒ and that scientists may be able to test for them. Previous Years, BSc Physics, Questions, University of Calicut, Information about admissions opportunities, last date for application. “If you observe an entangled quantum particle ” says Alice, “you get an answer,” says Betty. quantum systems is very di erent for the macroscopic systems of Classical Mechanics. Check how the prediction of the model matches the experimental results. However there is a deep mystery about why the Quantum Mechanical algorithm is so successful. When you take the test, you will mark your answers on a separate machine-scorable answer sheet. If you lost points on this question, please bring your exam to Professor Cramer and your score will be adjusted upwards 6 points (i. A manual for each experiment in. Griﬃths (Cambridge 2016) Use the textbook and the class schedule at the end of this document to prepare before each lecture and to work on the questions and exercises that will be the basis of the problem sets and tutorial quizzes. Do NOT write your class ID number on this page. Quantum Chemistry Exam 1 Solutions. you have convenient answers with quantum mechanics mcintyre solutions download PDF. Unit 8 Quiz--The Quantum Mechanical Model of the Atom: Multiple Choice B C Use the two dimensional plots of electron probability to answer questions 1 - 5 below. Problem 1). This science article is a stub. Here I have attached the Previous year question papers of Classical Mechanics which is taught in the First Semester. Then we’ll talk about early experiments to determine the properties of atoms. Answer each question in a separate booklet Candidates are reminded that devices able to store or display text. YES! Now is the time to redefine your true self using Slader's free University Physics answers. Quantum Mechanics (QM) Quantum mechanics is… • The set of rules obeyed by small systems (molecules, atoms, and subatomic particles) • One of the two greatest achievements of 20th century physics • The basis for new research into smaller electronic devices (e. Access study documents, get answers to your study questions, and connect with real tutors for PHYSICS 137B : QUANTUM MECHANICS II at University Of California, Berkeley. theory predicting discrete energy levels of electron orbitals, led to the theory of quantum mechanics taking over from classical physics at very small scales. Provide details and share your research! Successive amplitudes in quantum mechanics. Download University of Pune previous year question papers Semester 1 PDFs with solutions for M. Solve it to get Eigen functions & show that the Eigen values are discrete. Quantum Mechanics Chapter Exam Instructions. Then, add up your correct answers and enter. To get started finding quantum mechanics mcintyre solutions download, And you are right to find the biggest collection of listed. correctness of quantum mechanics? We describe the con-struction of a speciﬁc kind of quantum random number generator for which the answer to these questions is af-ﬁrmative. Start This Quiz You have {{ vm. The test problems require only simple calculations and focus instead on the ideas and formalism of quantum mechanics. RE: Quantum hacking questions for a sci-fi project By PESchoenberg - on August 18, 2019 So far, no one has shown experimentally that it is possible to eavesdrop a quantum system without disturbing it. The third rule limiting allowed combinations of the n, l, and m quantum numbers has an important consequence. You may start reading any chapter: if you ﬂnd it incomprehensible. Total testing time is two hours and fifty minutes; there are no separately timed sections. Qualitative Questions: 1. Quantum mechanics can only answer questions regarding the outcome of possible experiments. you have convenient answers with quantum mechanics mcintyre solutions download PDF. on the Hilbert space structure of Quantum Mechanics, on scattering theory, on perturbation theory, on Stochastic Quantum Mechanics, and on the group theory of elementary particles will be added as well as the existing sections expanded. a) Electromagnetic radiation is incapable of passing through water. But wait ! We will also post the pdf file as e-book in due course. If you don't see any interesting for you, use our search form on bottom ↓. How much further? Circle one: 0. Explain what do you mean by the term potential well. Another correct answer is that "the vacuum" is what is shaking. What are the shapes of s, p, and d orbitals respectively? s= spherical p = dumbbell d = cloverleaf 2. This is a course on Quantum Mechanics written and delivered by Prof. Chemistry Practice Test - Ch. This seemingly contradictory concept shows how weird quantum physics can be when compared to classical physics. The “snapshot of foundational attitudes toward quantum mechanics” taken by Schlosshauer, Koﬂer, and although a number of the questions (and/or answers) from. However, the reader could satisfy his curiosity, with help of keywords,. We permitted multiple answers per question to be checked, because in many cases the different answers were not, and could not be, mutually exclusive. postulate of quantum mechanics, and that every time you look at a digital watch, or touch a computer keyboard, or listen to a CD player, or interact with any other electronic device that has been engineered with the help of quantum mechanics, you are testing and vindicating this theory. An electron can seem to interfere with itself when passing through double slits. Mechanics is the branch of Physics dealing with the study of motion when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. It forces the number of subshells in a shell to be equal to the principal quantum number for the shell. 46-56 (2004) Summary Werner Heisenberg was one of the key players in the development of quantum mechanics. What are the quantum numbers that describe a. Quantum Mechanics Practice Test. In the previous lectures we have met operators: ^x and p^= i hr they are called \fundamental operators". It solves the Schrödinger equation and allows you to visualize the solutions. The mid-term exam is a take-home exam, and the final exam is administered in class. What you're lacking is two years of physics on the undergraduate point. Quantum mechanics is now a mature topic dating back more than a century. 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If no papers/answers are available, the module may be assessed by non-exam means. Mark the best answer A, B, C, D or E on the Answer Sheet. If you don't see any interesting for you, use our search form on bottom ↓. Principle of the Superposition of States. Here are my solutions to various problems in David J. quantum state of the apparatus must take into account the interactions with the environment in some statistical way. All students, freshers can download General Knowledge Physics quiz questions with answers as PDF files and eBooks. 5 = 30) Obtain the equation of continuity in Quantum mechanics. The Avengers Movie Free Download Hd. 3 nm, what is the energy and frequency of a photon of this light? Note: Planck's constant = 6. Choose your answers to the questions and click 'Next' to see the next set of questions. Quantum Mechanics: Questions 1-4 of 80. What is the maximum number of orbitals with: n = 4 l = 1 3 (the 4p orbitals) n = 2 l = 2 none (l must. 626 x 10–34 J·s, speed of light = 2. Quantum Mechanics Interview Questions & Answers If you are interested in studying the behavior of matter and energy, the wisdomjobs can guide you to develop a career in Quantum Mechanics. How many electrons are in a hydrogen atom? 2. Quantum Mechanics explains how your Psyche, Intelligence, Spirit, Soul, Spark, Mind, or Quantum Non-Local Consciousness controls your physical body and your physical brain. A radical new theory plays into that, proposing that parallel universes exist and interact with each other ‒ and that scientists may be able to test for them. Other books that I recommend include A Modern Approach to Quantum Mechanics by John S. Answer number 3: Classical mechanics does not give a satisfactory answer, why atoms are stable. The allowed energy states of a free particle on a ring and a particle in a box are revisited. 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Previous years MSc physics CAT entrance exam question papers with answers?-- [New] MSc Physics previous years question papers with solutions?. Shankar Principles of Quantum Mechanics in pdf form, in that case you come on to the correct website. Answer number 3: Classical mechanics does not give a satisfactory answer, why atoms are stable. Hydrogen has a red emission line at 656. The "snapshot of foundational attitudes toward quantum mechanics" taken by Schlosshauer, Koﬂer, and although a number of the questions (and/or answers) from. Quantum mechanics is a powerful framework for understanding the motions and interactions of particles at small scales, such as atoms and molecules. Previous years question papers for MSc in Physics? Previous years MSc physics CAT entrance exam question papers with answers?-- [New] MSc Physics previous years question papers with solutions?. It only takes a minute to sign up. How many orbitals are in the 4d subshell? 3 6 4 5. Orbitals and Quantum Numbers Practice Questions 1. The questions in the practice test in this book illus-trate the types of multiple-choice questions in the test. Derive an expression for Schrödinger’s Wave equation for a particle confined in a three-dimensional box. Directions: Answer all three questions. Quantum Chemistry Questions And Answers Pdf Chapter 1: Introduction to quantum mechanics. Linguistic interpretation of quantum mechanics: Quantum Language Shiro ISHIKAWA (ishikawa@math. Quantum mechanics solved problems pdf. Take the Quiz: Quantum Physics for Dummies. of units for a class of physical phenomena which we call mechanics, they are not a suﬃcient set of units if we want, in addition, to measure, say, temperature, or an electric charge. The descriptor \quantum" arises. Sakurai, Jim J. Electron waves MCQs, quantum physics quiz questions and answers for admission and merit scholarships test. "Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics" is an invaluable tool. your total number of correct answers in the space labeled “Total Correct” at the bottom of the page. Each week's notes come with a blog entry where you can ask questions and make comments. The Top and Best Engineering Mechanics Books Collections are listed in the below table as well as Engineering Mechanics Books PDF download link. Feynman and Alber R. Theory of everything: Is there a theory which explains the values of all fundamental physical constants, i. When solving numerical problems in Quantum Mechanics it is useful to note that the product of. The book is tailored to the needs of university students preparing for their university/competitive exams in chemistry. Choice of units for quantum mechanics (10 October 2011). Lets use an electron as the item trapped in a well (which is typically done). When you're done, try again to. General physics/quantum physics. of the electron from the nucleus, which is controlled by the principal quantum number, n. Some of the worksheets below are Quantum Mechanics Worksheets with Answers, the essential essential ideas of quantum mechanics, Solving the Schrödinger Equation, …, The Physics of Quantum Mechanics : Contents – What is Quantum Mechanics About?, Forging Mathematical Tools, Continuum Systems, Quantum Mechanics in Two and Three Dimensions, …. The greatest conceptual problem of quantum mechanics is its very foundation: the wavefunction. quantum mechanics questions pdf The third is a set of answer tables for multiple choice questions. Note that question 8 of this exam was originally graded with answer (d) as correct. " You may have noticed water waves often travel in packets. Quantum mechanics solved problems pdf. In a very schematic way, classical mechanics tries to compute how a particle travels from A to B. Explain what do you mean by the term potential well. KEY BENEFIT: Robert Scherrer's text provides a uniquely accessible and thorough introduction to quantum mechanics for readers. "Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics" is an invaluable tool. With captivating facts, images and stories on every page, the free Motion Mountain Physics PDF Textbook is written for students, teachers and everybody curious about motion in nature. However, it is answer (b) that is correct. Zurek Quantum mechanics works exceedingly well in all practi- cal applications. Quantum mechanics can only answer questions regarding the outcome of possible experiments. Quantum mechanics can be thought of roughly as the study of physics on very small length scales, although there are also certain macroscopic systems it directly applies to. Energy is emitted in discrete multiples of \(h\nu\), where h = Planck's constant. List of equations in quantum mechanics Jump to A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. Engineering Mechanics Pdf 1st year Notes Pdf. What is the de Broglie wavelength for an electron moving at 2. Questions and Answers The value of the Magnetic Quantum Number is any number between -l and l. Problems and Solutions on Quantum Mechanics. Exams Download Course Materials; Both exams are open-book, open-notes, but you should not consult other people about the exam questions. Our online quantum physics trivia quizzes can be adapted to suit your requirements for taking some of the top quantum physics quizzes. Practice Final Exam. jp) Department of mathematics, Faculty of science and Technology, Keio University, 3-14-1, Hiyoshi, Kouhokuku, in Yokohama, 223-8522, Japan Abstract This is the lecture note for graduate students1. What KE is imparted to recoiling electron? Solution: In this question, we are dealing with the famous Compton effect. Answerallquestions inSection Aandonly twoquestions inSection B. It only takes a minute to sign up. com is the place to go to get the answers you need and to ask the questions you want. Walk to a wall and you can't walk through it. A photon has a definite energy hv. quantum mechanics questions pdf The third is a set of answer tables for multiple choice questions. How many orbitals are possible at the 3rd energy level (n=3)? 4. 998 x 108 m/s 2. Quantum Mechanics Forums - Ask an expert about quantum mechanics Quantum Mechanics, Quantum Physics, Philosophical Questions, Quantum Mechanics, Semantics. , Publication. Shankar Principles of Quantum Mechanics Solutions Please visit Dropbox support if you have any questions. Questions of this kind deal with only one aspect of quantum theory. The questions in the practice test in this book illus-trate the types of multiple-choice questions in the test. Parity: a wavefunction has definite parity if ψ(−x) = ±ψ(x); this requires a symmetric potential, V(−x) = V(x). CHEMISTRY 151 - QUANTUM NUMBERS KEY 1. 15 B37 2006) Schaum’s outline of theory and problems of quantum mechanics / Yoav Peleg (QC174. The ideas behind quantum mechanics often appear quite strange. In most of the popular books on the market, however, the bulk of the. Sound, light, heat, quantum physics and so. Free Download e-Books When the scan completes, it will open two notepad windows. The foundations of quantum mechanics (PDF) Chapter 02 Linear motion and the harmonic oscillator (PDF) Chapter 03 Rotational motion and the hydrogen atom (PDF) Chapter 04 Angular momentum (PDF) Chapter 05 Group theory (PDF) Chapter 06 Techniques of approximation (PDF) Chapter 07 Atomic spectra and atomic structure (PDF) Chapter 08. Sakurai, Jim J. And being good at diagnosing periodicity has a lot to do with factoring. of information, and the probability of outcome x 2f0;1g2 is j xj2. 1 Wave packets Waves can be long with many vibrations, as when you hum, or they can be short, as in a shout. Solution: a) By the famous Einstein formula (mass-energy equivalence) we have: 𝐸=𝑚𝑐2. Each question is followed by the targeted learning objective(s) from the curriculum framework. It solves the Schrödinger equation and allows you to visualize the solutions. Quantum mechanics is based on Schrödinger’s wave equation and its solution. Updated on July 17, 2012 as the quantum wave process and every event has a probability to occur according to quantum mechanics. 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Quantum Mechanics Principles Steps Toward Quantum Theory Photoelectric Effect Some Handy Integrals Complex Waveforms, eix=cos x+isin x Complex Waveforms- Euler Identity Proof Classical Harmonic Oscillator Particle in a Box Expectation Values-Particle in a Box Heisenberg Uncertainty Principle: Gaussian Distribution. HW: Quantum Mechanical Model of the Atom Practice 1. Physics 143a: Quantum Mechanics I Spring 2015, Harvard Section 3: Particle in a Box and Harmonic Oscillator Solutions Here is a summary of the most important points from the recent lectures, relevant for either solving homework problems, or for your general education. Quantum Mechanics Quantum Mechanics- Syllabus January 2009 • Expect the leader to ask questions, rather than answer them. com/2017/11/quantum-physics-hc.