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. B

    Q3: How do we measure rotational degrees of freedom in quantum mechanics?

    I have a basic question that still is not clear to me. In QM, various operators are generators of something (ie. momentum is a generator of linear translations, Ang. Mom the generator of Rotations and such) Question 1: Let us look at L, or a component, say Lz. When we operate on a...
  2. T

    QM 1-D Harmonic Oscillator Eigenfunction Problem

    Homework Statement A particle of mass m moves in a 1-D Harmonic oscillator potential with frequency \omega. The second excited state is \psi_{2}(x) = C(2 \alpha^{2} x^{2} + \lambda) e^{-\frac{1}{2} a^{2} x^{2}} with energy eigenvalue E_{2} = \frac{5}{2} \hbar \omega. C and \lambda are...
  3. jedishrfu

    Leonard Susskind's new book on QM is now out

    Leonard Suskind's new book on Quantum Mechanics: The Theoretical Minimum is now available. I bought a copy at the local Barnes and Nobles. It looks pretty good after briefly scanning it but I'll know more once I begin reading. Can it be placed in the list of recommended books that Greg started...
  4. U

    Is something wrong with statistical interpretation of QM?

    The probabilistic nature of QM seems apparent(in theoretical formulation as well as experimentally), then why do most of the physicists give the credit of in-determinism to the nature itself and look for many worlds, abruptly collapsing observer conscious experiment setups, and the likes...
  5. X

    Recommendations for Study Materials [QM]

    Hello all, I'm taking my first actual quantum course this semester. I went over "briefly" some quantum mechanics Fall of 2012 in a Modern Physics course during my sophomore year, currently I'm a junior. To get straight to the point, this course is making me miserable. I had high hopes for...
  6. protoplast3r

    Dividing line between QM and CM?

    Hey guys, I study biophysics, so maybe this is a sophomoric question. I've done a cursory, albeit fruitless search of the forums and the web, I think I don't know how to properly ask the question... I was wondering if there is some sort of limit -- I would assume a given mass of an object...
  7. B

    How are transistors and QM tied

    I know that transistors work using QM, but I don't know how, can someone explain this to me?
  8. M

    QM solutions to the Schrodinger Equation

    Homework Statement Here's something that's confusing me. Say we have a potential V(x) = Vo if x < 0, x > a and V(x) = 0 if 0 < x < a (yes I know the notation with greater than/equals etc isn't totally correct, but you know what I'm talking about.) In the middle section, ψ'' +...
  9. J

    Can't Identify Variable in QM Question

    Hello, my question is a simple one: I am attempting to do problem 2.31 in Griffiths' QM book (latest edition). The question states, "The Dirac Delta function can be thought of as the limiting case of a rectangle of area 1, as the height goes to infinity and the width to zero. Show that the...
  10. S

    Where's the first place I should go to learn QM?

    I need the math. I get a little bored doing the low level stuff, and want to jump into it. As long as I'm interested I won't get bored. I started the other thread discrete wave functions below, and realized I like everything about QM. Hopefully I don't get bored. Sorry I just read the forum...
  11. G

    Assume QM is realistic but non-local: Explain superposition?

    Hi, The violation of Bell's inequality says that quantum mechanics can't be both local and realistic. Let's assume it is realistic but non-local. How does this explain the fact that a single particle can be in a superposition that collapses to a particular state when measured? Since we only...
  12. C

    Step on Weinberg's QM Book (pp. 154-155)

    Hello all! On the problem of taking elements of different (degenerated-)state vectors that do not vanish on the perturbation matrix, Weinberg uses the following approach, when dealing with the Zeeman effect: In this way, he goes from the first to the second equation shown as attachments...
  13. L

    Where Can I Find Comprehensive Notes on Quantum Mechanics Interpretations?

    Does anyone know good notes or a book on quantum mechanics that covers well the interpretational issues? Especially, which deals also with the last fifty or sixty years, i.e. that has Bell, decoherence, GHZ, Aspect experiment, Mach-Zehnder interferometer, delayed-choice, mesocopic Schrödinger...
  14. S

    What does QM hint about time-space?

    Does QM hint at time-space being an emergent, rather than a fundamental, property/constituent of nature? In what ways? Electromagnetic (EM) fields are assumed to pervade all of time-space. Which is more fundamental?
  15. D

    I - what are prerequisites for studying QM?

    i need help -- what are prerequisites for studying QM? i have always had an interest in different fields of science, but lately i have become extremely interested in quantum mechanics. i know that there may be different subdivisions of the field, but I'm more interested in like theoretical...
  16. D

    Is it likely engineers will ever need to go beyond basic QM?

    It seems the most advanced physics engineers are using is basic quantum mechanics. Is it accurate to say this is the "final frontier" of engineering? The field of particle physics, for example, has been established for nearly 50 years now and there are still no practical uses of the incredible...
  17. M

    The Classical Path, QM Path Integrals and Paths in Curved Spacetime

    "The" Classical Path, QM Path Integrals and Paths in Curved Spacetime Hey Guys! I've got an exciting question! It's been burning on my mind for years, but I think I can formulate it now. It's not so much a specific question, but rather a physical story which perhaps this thread can uncover...
  18. morrobay

    What Interpretation/Model of QM Predicts Bell Inequality Violations ?

    Are there any modern interpretations of QM that predict the correlations in a Bell Inequality violation ? Preferably a local non realistic model based on mechanisms.
  19. K

    Understanding Mass and Vectors in Quantum Mechanics: The Role of the Higgs Field

    Before measurements, quantum states are vectors in Hilbert space and there may not even be momentum or position chosen before wave function collapse or measurement. I'd like to understand how mass or the higgs field couple to wave function. Can higgs home into the specific ray or vector in...
  20. A

    Van del waals interaction in qm

    Hello I read the follow paper about van del waals interaction in quantum mechanics http://www.damtp.cam.ac.uk/user/gold/pdfs/teaching/van_der_waals.pdf In this paper the potential V= e^2/R + e^2/(R+y)+e^2/(R-x)+ e^2/(R+y-x) is aproximated to V \approx -2 e^2/R^3 xy with R>>|x|,|y| why...
  21. L

    Understanding Potential Energy in QM

    Hi all, I'm having conceptual troubles understanding the significance of the potential energy term in Schrodinger's equation. More specifically, the physical meaning of the potential "wells" is not clicking with me; my textbook is not making this very clear. For clarity, consider an...
  22. Superposed_Cat

    Where to learn the matrix formulation of QM

    Hi, material on learning the calculus way are plentiful but I can't find anywhere to teach me the matrix way, any links? I can't even find out how to represent the Hamiltonian as a matrix. Thanks in advance
  23. D

    Bra-kets and operator formalism in QM - Expectation values of momentum

    Homework Statement sup guys! I think I've solved this set of problems, but I was just wondering if I've done it right - I have no way to tell. I'll put all the questions and answers here - plus the stuff I used. So could you please tell me if there's any mistakes? Here it is - using Word...
  24. G

    Open Problems in Interplay between QM & 2nd Law of Thermodynamics?

    What are some open problems in the interplay between Quantum Mechanics and the 2nd Law of Thermodynamics? thanks
  25. D

    Finding normalized eigenfunctions of a linear operator in Matrix QM

    Homework Statement Hey everyone! The question is this: Consider a two-state system with normalized energy eigenstates \psi_{1}(x) and \psi_{2}(x), and corresponding energy eigenvalues E_{1} and E_{2} = E_{1}+\Delta E; \Delta E>0 (a) There is another linear operator \hat{S} that acts by...
  26. B

    What is a Possible Normalized Spin Wave Function?

    Homework Statement A number of spin 1/2 particles are run through a Stern-Gerlach apparatus and when the emerge they all have the same spin wave function (ψ1, ψ2)τ and 9/25 are in the +z direction and 16/25 are in the -z direction with the normal basis column vectors for +z and -z...
  27. G

    Wikipedia comparison of interpretations of QM

    Hi, I'm studying http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comparison_of_interpretations but have trouble with the apparent differences of the key concepts: * deterministic - unique history * wavefunction real - hidden variables - counterfactual definiteness I...
  28. C

    Can a Specific Width Parameter Ensure a Bound State in a 1D Quantum System?

    Homework Statement Consider a one-dimensional quantum system described by the potential: $$V(x) = -V_o + \frac{1}{2}mw^2x^2\,\,,V_o > 0\,\,\text{for}\,\, |x| < b\,\,\text{and}\,\,0\,\,\text{otherwise}$$ Show that the state described by: $$\psi_{-}(x) = R_{-}...
  29. M

    Division between QM and Interpretations

    Trying to relate a bit better to where QM stops, and Interpretations begin. Especially with respect to Decoherence. Is Decoherence seen as a measurable phenomena, or, just as a "possible" explanation for measurable phenomena? Obviously when I mark a path in a 2 slit experiment I cause...
  30. C

    Is This Wave Function an Eigenfunction of Energy and Momentum Operators?

    I've been wrestling with this question for a while and can't seem to find anything in my notes that will help me. Homework Statement Determine whether the wave function \Psi (x,t)= \textrm{exp}(-i(kx+\omega t)) is an eigenfunction of the operators for total energy and x component of momentum...
  31. B

    Challenges in Merging GR and QM from a Lagrangian Perspective

    My first of many GR questions :cool:: If electromagnetism can be incorporated into the standard model, where I think of electromagnetism as derivable from an action principle ala Landau-Lifshitz, at what point does this process stop working when you use gravitation? I was thinking the...
  32. K

    PDE - Boundary value problem found in QM

    This is a quantum mechanics problem, but the problem itself is reduced (naturally) to a differential equations problem. I have to solve the following equation: \frac{\partial}{\partial t}\psi (x,t) = i\sigma \psi (x,t) where \sigma > 0 The initial condition is: \psi (x,0) =...
  33. N

    Schrödinger or Heisenberg Picture for Density Matrix Evolution?

    Homework Statement Hi The density matrix evolves as \dot \rho = -\frac{i}{\hbar}[H,\rho] but is this equation written in the Schrödinger or Heisenberg picture? I'm not entirely sure how to figure this out. In my book it just mentions the equation, not how it is derived (which may have given...
  34. J

    Are Quantum Mechanics and Cosmology Directly Linked?

    I recently read an article (http://vixra.org/abs/1308.0143) written by an acquaintance, Dr Dimitar Valev and wanted opinions on its relevance . Basically, dimensionless ratios are derived from equations based on both the Planck constant and the Hubble constant. Thus, Quantum Mechanics and...
  35. O

    Eigenvector proof from Dirac's QM

    Hi everyone, I'm currently working my way through Dirac's Quantum Mechanics, and I found this proof really irritating. We're trying to demonstrate that any eigenket can be expressed as a sum of eigenkets of a real linear function \xi which satisfies the equation \varphi(\xi) =...
  36. L

    Admissions Recommended Book For Entry to QM

    Hi guys, The other day I was struggling to to grasp some of the concepts in QM. I realized I would never understand without understanding the math. From what I know the following book is what they give to first year university students. I'm on page 20, and I am struggling. But I'm determined to...
  37. D

    QM - Transmission coefficient for square well

    Homework Statement A steady stream of 5 eV electrons impinges on a square well of depth 10 eV. The width of the well is 7.65 * 10^-11 m. What fraction of electrons are transmitted?Homework Equations The following equation for the transmission coefficient, T, is given: T = [1 + \frac{V_0 ^2...
  38. S

    Quantum Mechanics Effects: Proton vs Up Quark

    I'm pretty sure a proton's location does not have much quantum uncertainty but an up quark does. So qm uncertainty begins around 10^-15m and is full blown at 10^-18m If my numbers are wrong please let me know.
  39. I

    Best college level text book for beginners of QM

    I have read a lot of stuff on Quantum Mechanics and there seem to be a lot of outlandish theories on the web mixing QM with every religion in a search for god as the great observer. I would really love to get my hands on a good college level textbook that explains the more supported theories...
  40. A

    Error in Griffiths QM: completeness of stationary states

    According to Griffiths QM book, after he derived the stationary state solutions to the Schrodinger equation for a particle in an infinite potential well, which are just functions of sine, he claims that these stationary solutions are orthogonal and complete. I agree that they are orthogonal...
  41. L

    Trying to make the connection with QM as a 1 parameter QFT

    I'm seeing lots of underlying connections between the canonical formulism of QFT and QM. But I'm getting a bit confused by their differences. I'll just write down my thought process: QM is a one parameter system (t) in a space with three quantized operators (x,y,z) QFT is a four parameter...
  42. Astrum

    Best Intro to Quantum Mechanics: Griffiths vs Dirac

    What is the best intro to QM? I was settled on Griffiths, but it seems there are only two kinds of people in this world, those who recommenced Griffiths, and those who strongly don't recommended it. I'll give a bit of background, so I can get the best possible recommendations. I'm...
  43. andrewkirk

    Seeking a non-technical book on the weirdness of QM

    I am in a philosophy club where we meet to discuss a topic each month. Next month I have undertaken to kick off a discussion on the philosophical implications of quantum mechanics. I expect interpretations of QM, especially things like MWI, to be a significant part of that. I need to find...
  44. L

    Neutron Beam Width after localization via a slit in a sheet (QM)

    Homework Statement A parallel beam of neutrons with speed 200m/s is incident on an absorbing sheet with a slit of width 0.01mm. Calculate the width of the beam 10m behind the slit. Hint The slit localizes the neutrons transversely (y) to their propagation direction x. The resulting ΔPy gives...
  45. I

    What do waves represent in QM?

    i get that the Waves represent the probability density of the object, but a wave has a crest and a trough. What does the specifically does the trough represent? what specifically does the crest represent?
  46. hilbert2

    QM Inverse Problem: Finding V(x)

    Let's say we have a one dimensional single particle system that is described by a SE -\frac{\hbar^{2}}{2m}\frac{d^{2}}{dx^{2}}\psi(x)+V(x)\psi(x)=E\psi(x) We do not know what the potential energy function V(x) is, but we know that the eigenvalues spectrum is E_{n}=kn^{\frac{3}{2}}...
  47. M

    QM: Clarifying Pauli Exclusion Principle, State of System

    Just want to clarify my understanding of these things. Fermions obey the Pauli Exclusion Principal, meaning meaning only one particle can occupy a single state. This means the wave function is anti-symmetric under particle exchange. That's the part that isn't making much sense. Is it because...
  48. L

    Operator Theory Problem on Momentum Operator (QM)

    Homework Statement Given the operators \hat{x}=x\cdot and \hat{p}=-i\hbar \frac{d}{dx}, prove that: [\hat{x}, g(\hat{p})]=i\hbar \frac{dg}{d\hat p}Homework Equations None. The Attempt at a Solution I have very little idea on how to begin this problem, but I don't want a solution, I simply...
  49. J

    [QM] Help understanding this bra-ket solution

    Hello, I am working my way though Sakurai's book on Quantum MEchanics and am having some problems understanding the bra-ket notation. I keep believing I understand everything there is to it but then he will do something in a single line that I cannot understand. This is one of them. If...
  50. G

    Do we really need to unify GR and QM?

    Decades of work are being put in trying to find a unified theory which can accommodate both General Relativity and the Standard Model. I guess that the attractive of a unified theory is more than justified, but does it really need to be the case? Is it possible that the universe works really...
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