Qm Definition and 1000 Threads

The hybrid QM/MM (quantum mechanics/molecular mechanics) approach is a molecular simulation method that combines the strengths of ab initio QM calculations (accuracy) and MM (speed) approaches, thus allowing for the study of chemical processes in solution and in proteins. The QM/MM approach was introduced in the 1976 paper of Warshel and Levitt. They, along with Martin Karplus, won the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems".

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  1. A

    Should the average undergrad be able to solve most of Griffiths' QM problems?

    I am a third year physics major and am studying quantum mechanics using Griffiths' textbook. I can do most of the problems with one star or no stars with relatively little effort, but a lot of the problems with three stars I find very difficult and I cannot do them at all. For the average...
  2. S

    Normalization of wave function (Griffiths QM, 2.5)

    Homework Statement A particle in the infinite square well has its initial wave function an even mixture of the first two stationary states: \Psi(x,0) = A\left[ \psi_1(x) + \psi_2(x) \right] Normalize \Psi(x,0). Exploit the orthonormality of \psi_1 and \psi_2 Homework Equations \psi_n(x) =...
  3. T

    Why not formulate QM in terms of |ψ| squared?

    I'm beginning to study QM, and as I understand all the information we can get out of system with 1 particle is the probability distribution function (which has position and time as variables). By knowing the wave function it's possible to know the probability distribution function, but that's an...
  4. M

    Why all operators in QM have a Hermitian Matrices

    Why all operators in QM have a Hermitian Matrices ?
  5. A

    Do QM and Thermodynamics interact?

    I'm actually quite scared of asking this due to my very basic knowledge regarding Quantum Mechanics. Actually, this is my first hiccup: is there a difference between Quantum Physics and Quantum Mechanics? I always thought one was the theoretical investigation and the other the application but...
  6. B

    Measuring "Velocity" in Quantum Mechanics: Meaning of the p/m Operator

    Classically, a direct measurement of velocity requires two measurements - position at time t1 and position at time t2. In QM such a measurement is not meaningful, since measuring position at time t1 would necessarily affect the particle (i.e. cause it to collapse to some position eigenstate)...
  7. T

    Gauge Symmetry in Quantum Mechanics (QM I) Explained

    Hi all, I'm taking graduate level QM I and trying to wrap my head around the notion of gauge symmetry. For some reason I've struggled with this concept more than others. I don't really have a specific question; I'm more looking to see if someone has a succinct explanation of the relevant...
  8. A

    QM Puzzle: Can One Particle Have Multiple States?

    I was taught that a particle is assigned to a unique quantum state. As a specific example, two bound electrons can't have the same quantum numbers in an atom. And likewise one and only bound electron is assigned to one quantum state in an atom. Yet, I am reading several solid state books and...
  9. C

    Is objective reality possible under orthodox QM?

    One of the postulates of QM is that the physical state of any system (with any number of constituent particles) corresponds to a Hilbert state vector ψ. So an isolated system that includes an object to be observed, the observing apparatus, and also the human observer himself is also represented...
  10. W

    Why Are Orbital Angular Momentum Quantum Numbers Restricted in H2 Molecule?

    Hey, I cannot solve this problem. Please help me. In the H2 molecule, the Pauli exclusion principle demands that the wavefunction of two protons be antisymmetric under the interchange of the two proton coordiates. Based on this, explain the (a) In the spin-triplet states of two protons...
  11. A

    Quantum Mechanics and Classical Mechanics: Is there a connection?

    What is the connection between QM and classical mechanics? This has never been obvious to me, but it seems that it would be desirable that we should be able to derive the laws of CM from QM, but I've never really seen that done convincingly. Can you actually show that a very large quantum system...
  12. D

    Questions about information in QM

    Several questions. 1. Do different observers (with the same knowledge) in different inertial frames agree on the number of states of some specific system? 2. The same question for the different accelerated frames; 3. The most difficult one Say, Alice observes some system X with N particles...
  13. M

    Which Book is Best for Learning Quantum Mechanics?

    Hello! I have been told that Zettili's book is the best. How much is that true? And can I follow it and still be capable of solving problems posted in exams (knowing that my Prof is working in other books.. ) I want to be able to solve ANY exercise at the end of the semester. Your...
  14. J

    Quantum Mechanics Before Classical Mechanics: Implications and Speculations

    Just an abstract question here. How different do you think the world would be if we were taught quantum mechanics before classical mechanics, given the prerequisite that we already have a good knowledge of the mathematics? Of course, it's a highly unlikely scenario, but an interesting one none...
  15. S

    Understanding the 2012 Noble prize in QM

    Noble prize in QM for 2012 1. Would someone like to summarize the research and results? 2. how can single quantum particles be observed without destroying them? 3. how were they able to show both states at the same time? 4. were the two physicists entangled at 68?...;)
  16. B

    Check Answers to Quantum Minima Qs: In-State Vector Operator

    I'm trying to "sure"up my Quantum Mechanics and found an sheet of mostly conceptual review questions. A sort of "Quantum minima". I'd like to check my answers to a couple of these. Firstly: In terms of state vector the wavefunction is the expansion coefficient (probability amplitude) of a...
  17. O

    QM: measurement vs interaction

    I'm just wondering... Regarding the single & double slit experiments... Why does every interpretation say that the photographic screen is 'measuring' the position of the particle traveling towards it? Why not say that the photographic screen interacts with an electron that is spread out...
  18. T

    Problem understanding Green's function equality in Messiah QM II

    Hi, It's about green's function in the book Messiah - Quantum Mechanics II - Chapter 16.3.2 (see http://books.google.de/books?id=OJ1XQ5hnINwC&pg=PA200&lpg=PA202&ots=NWr6A89Mkt&dq=messiah+quantenmechanik+kapitel+16.3&hl=de). The book actually is in german, but I guess that doesn't matter...
  19. K

    QM Fourier Transform and Integral rules

    Show G(k)=\sqrt{2π}g1(k)g2(k) Given that G(k) is the Fourier transform of F(x), g1(k) is Fourier trans of f1(x), g2(k) is Fourier trans of f2(X) and F(x)=^{+∞}_{-∞}∫dyf1(y)f2(x-y) SO FAR G(k)=1/\sqrt{2π}^{+∞}_{-∞}∫F(x)e-ikxdx <-def'n of Fourier transform...
  20. J

    Time Dependence in Pictures of QM

    I have a question about time dependence in the different pictures of QM. In the Schrodinger Picture, I've read that the time dependence is in the state vector, but one can construct Hamiltonians and other operators that are time dependent in the Schrodinger Picture. For instance, one can...
  21. C

    What is the Operator for Absolute Value of Momentum in Quantum Mechanics?

    Hi, I am looking for the operator representing the absolute value of a particle's momentum. In other words: the square root of the laplacian (preferably in 3 dimensions, but 2 would also be fine). I am aware, that integral formulas exist for this operator, but is it possible to express it...
  22. A

    Tricky integral in QM variational method

    Homework Statement Find the variational parameters \beta, \mu for a particle in one in one dimension whose group-state wave function is given as: \varphi(\beta,\mu)=Asin(βx)exp(-\mux^{2}) for x≥0. The wavefunction is zero for x<0. Homework Equations The Hamiltonian is given as...
  23. M

    Visualising mathematical concepts in QM - comments needed

    Hi, I'm unsure if I'm posting this in the correct place, so apologies in advance if not. I looked at the study board, but the post template doesn't apply to my question. I'm a layperson who had previously only read popular science books on QM, but has recently been watching some more...
  24. Drakkith

    Do you use QM in Conjunction With QED/QCD?

    Do you still use QM in conjunction with the other theories? Is QM kind of like the basic theory that the others rely on? (Hopefully those questions make sense)
  25. SnotRocketSci

    What would you consider to be the most quintessential equations of QM?

    I am an UG student majoring in Physics. I am just starting classical coursework, but I have had, for the past 10 or so years, a great interest in Quantum Theory. I have read nearly every popular-level (read: very little, if any, math) book published in the last 15 years on the subject, but just...
  26. E

    QM & CTCs: Examining the Possibility of Closed Time-Like Curves

    If QM requires a constant universal time, does this rule out closed time-like curves?
  27. A

    Do you think this theory/website REALLY prove Many World Interpretation of QM?

    Hello all, On one forum I found this link: http://oyhus.no/QM_explaining_many-worlds.html claiming to demonstrate correctness of Many Wordls interpretation of QM. On the one hand - seems like well presented arguments. On the other hand: it claimes to be discovered in 1990,and it seems...
  28. C

    Psychology of QM Interpretations Studied?

    Does anyone know of a psychological study done of the various people who take different positions in the debates about interpretation of quantum mechanics? I mean something that would analyze the philosophical reasons for the arguments, and the emotional drives that might lead physicists to...
  29. C

    Unitary equivalence of QM (not for energy?)

    Since all the observables in QM is on the form \langle \alpha |A| \beta \rangle where A is an observable, one can transform the observables and states like A \to A' = UAU^{-1} \ \ \ |\beta \rangle \to |\beta '\rangle = U |\beta \rangle where U is a unitary transformatioin. These...
  30. G

    QM Notation Deleted | Easy Solutions

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  31. D

    Need recommendation for good popular science book on QM

    If such a thing exists, what is a good popular science book for quantum mechanics? Multiple book choices would be accepted. Not looking for textbooks, more something you can lend to people who don't have science degrees but who are keenly interested in the subject. In an ideal world it...
  32. G

    Is the unpredictability of clouds due to QM uncertainty?

    As I see it the unpredictability of clouds can have two causes: 1. quantum indeterminacy or 2. Clouds are classical objects but they are so complicated that they cannot in practice be predicted I'm inclined to think 1 is correct. Correct me if I'm wrong but I'm pretty sure protons'...
  33. C

    General Question About Path Integral Formulation of QM

    Hello all, I will be learning about the path integral formulation, among other topics, in an advanced QM class during this upcoming semester, so I read ahead a little. I understand that, essentially, the propagator between two points in spacetime is the normalized sum of exp(i*2pi*S/h) over...
  34. C

    Time Dilation in QM: Elevator Experiment

    Lets say I have 2 elevators And I have the same experiment in both. Now the first elevator goes into free fall in a constant gravitational field. Now a little bit later the second elevator goes into free fall. Now as the second elevator goes into free fall its wave function is the same as the...
  35. S

    Linear Algebra for Quantum Mechanics Prerequisite

    I was going through Linear Algebra which is recommended as a prerequisite to Quantum Mechanics. The topic of LA is vast and deep. So I wanted to know which (specific) topics of LA should be covered as a prerequisite to QM.
  36. J

    I'm having trouble with an integral for my QM senior thesis

    I have been working through a method of solving the Time-Dependent Schrodinger Equation. I'm trying to learn this techniques before I actually jump into my project, however, I have come to an integral that I have been trying to do but can't think of a way to approach it. Mathematica could not...
  37. G

    Applications of Linear Algebra in Advanced Math: Chapter 6 Overview

    this is the final chapter of my Linear Algebra book. It looks like they're just exploring how LA is used in other more advanced math. I have a feeling that it is not very useful for QM which is what I want LA for.
  38. K

    QM: What are Tensor Operators & How to Understand Georgi's Definition?

    Hello! I´m trying to read Georgi's book on Lie algebras in particle physics but am confused about the start of chapter 4. Georgi writes that "A tensor operator is a set of operators that transforms under commutation with the generators of some Lie algebra like an irreducible representation of...
  39. M

    Shankar, Ballentine or Zettili for a first book on QM?

    All three seem to be loved, mathematically rigorous, and appropriate as undergraduate-level texts. I have a good knowledge of classical physics, ODEs and PDEs, linear algebra and multivar calculus, but no knowledge of analytical mechanics or QM. Some opinions on these or other recommendations...
  40. N

    Is the Factorization of Product Expectation Values Valid in Steady State?

    Homework Statement Hi I have read a paper, where they want to find the average number of photons in a cavity. They have an expression for \langle{\hat a}\rangle, and then they use \langle{\hat a}\rangle^* = \langle{\hat a^\dagger}\rangle to find \langle{\hat a^\dagger \hat a}\rangle. I agree...
  41. N

    QM: Master equations and derivatives

    Homework Statement Hi I have a technical question regarding the following paper: http://arxiv.org/pdf/quant-ph/0602170v1.pdf In it they derive an equation for \left\langle a \right\rangle (equation #5) from the master equation (equation #2). My question is how they do this. Here is what...
  42. N

    Is the Expectation Value Relation for QM Operators Valid?

    Homework Statement Hi My book uses the following in a calculation \left\langle a \right\rangle \left\langle {b^\dagger } \right\rangle + \left\langle {a^\dagger } \right\rangle \left\langle b \right\rangle = 2\operatorname{Re} \left[ {\left\langle a \right\rangle \left\langle {b^\dagger...
  43. I

    Role of hermitian and unitary operators in QM

    Which is the role of hermitian and unitary operators in quantum mechanics and which operator is neither hermitian nor unitary
  44. V

    What math to review before taking QM?

    I'm about to take introductory quantum mechanics next semester and was wondering what I should review from linear algebra? I took it 2 years ago
  45. G

    Using imaginary time to unify QM and GR

    I find this passage from A Brief History of Time a bit hard to believe. When he talks about using imaginary time for the purposes of calculation, is it the same like in the Schro eq which uses an imaginary number? How plausible is the following passage? Is using imaginary time a common practice...
  46. G

    Did Feynman unify special relativity with QM

    did feynman unify special relativity with QM or was it mostly a group effort and he just made some important contributions? did he make the decisive step just as leibniz and Newton made the decisive step with calculus? i watched a documentary about him and i couldn't get what his central claim...
  47. N

    Why is Griffiths not a good introduction to QM?

    I've seen quite a few people on this forum agree that Griffiths is not a good book to learn QM from. But I was wondering what reasons people would give for it. (Personally I don't feel I can give an in depth critique since I've only sampled his book. I rather liked his explanation of...
  48. S

    Why don't all observables commute in QM?

    In classical physics, all observables commute and the commutator would be zero. However this is not true in Quantum Mechanics, observables like position and momentum (time and frequency/energy) don't commute. Why? Is it because the (probability) wave functions/forms of position and momentum...
  49. S

    What's a thorough QM book besides Dirac?

    Hi, PF. I've got a question for you. Maybe this would be better posted in the science education or discussion sections, but it's directly related to QM. I'm just finishing up my undergrad coursework and I've taken QM using Griffiths. It's an okay book, but it does a bit of jumping around, and...
  50. K

    Some intuiontal questions concerning Sakurai's QM.

    Some intuitional questions concerning Sakurai's QM. Hello! I've just started reading Sakurai 's 'Mordern Quantum Mechanics' and open this thread for smaller intuitonal wonderings / questions. Some of them I might be able to solve myself with some help from you guys and others are of the sort...
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