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. MikeGomez

    Does Quantum Mechanics Explain the Fuzziness in Light Reflection?

    From this video of a Feynman lecture: At 39:30 he (Feynman) draws a line from the eye to the mirror, and then continues the line through the mirror, to represent where the image appears to come from (it appears to come from behind the mirror). Here he is showing the classical way of...
  2. fluidistic

    Ritz method in QM applied to a particular problem

    Homework Statement Using my classnotes and what the professor did, it is not clear to me as how I must tackle the following problem. I'm given the potential ##V(x)= V_0 \left ( \frac{x^2}{2} -K \right ) e^{-a x^2}## where a>0. I must estimate via Ritz method the ground state energy. I must use...
  3. fluidistic

    Expectation value of kinetic energy (QM)

    Homework Statement In a QM problem I must calculate the expectation value of the kinetic energy, namely ##\langle \Psi _c ,\frac{ \hat { \vec p } ^2}{2m} \Psi _c \rangle##. Where ##\Psi _c=ce^{-\alpha x^2}##. Homework Equations ##\int _{-\infty}^\infty \exp \{ -a x^2 +bx \} dx =...
  4. S

    Quantum Bayesian Interpretation of QM

    Any comments (pro-con) on this Quantum Bayesian interpretation of QM by Fuchs & Schack ?: http://arxiv.org/pdf/1301.3274.pdf
  5. fluidistic

    Probability, QM, harmonic oscillator, comparison with classical

    Homework Statement I must calculate the probability that the position of a harmonic oscillator in the fundamental state has a greater value that the amplitude of a classical harmonic oscillator of the same energy.Homework Equations ##\psi _0 (x)=\left ( \frac{m \omega}{\pi h } \right ) ^{1/4}...
  6. tom.stoer

    Stability of atoms in QM / QED

    It is often stated that quantum mechanics is able to explain the stability of atoms. I think most explanations are cheating b/c the compare apples and oranges. There are two reasons in classical theory which indicate that atoms should be unstable: A) there is no minimum for the orbit; the...
  7. J

    Accurate equations vs. accurate models in QM

    In QED, Feynman says: "The situation today is, we haven't got a good model to explain partial reflection by two surfaces; we just calculate..." I've been frustrated in that I'm still not clear if this is the case (is there still no model to explain the behavior). A similar dynamic seems to...
  8. C

    At what point does gravity become incompatible with QM?

    Is there some fuzzy area between the macroscopic and atomic worlds where gravity "still sort of works," or is it a dramatic cut off? I never understood this whole idea that it suddenly stops making sense at the quantum level. Does it start making progressively more sense as you increase the scale?
  9. H

    Exploring the Fundamental Postulates of QM: Are They Truly Ad-Hoc and Strange?

    I find the fundamental postulates of QM very ad-hoc and strange. Compare them to the fundamental postulates of special relativity, special relativity naturally arises out of classical electromagnetism and the equivalence of all inertial frames, while QM seems to come out of nowhere.
  10. R

    How to exponentiate a 3*3 matrix with all diagonal entries equal to zero?

    QM--- matrix exponentiation Homework Statement \ How do you go about exponentiating a 3*3 matrix? for example if you have <θ,∅|exp(-i*∅*Ly/h)|l,m> Homework Equations I know how to exponentiate a two cross two diagonalized matrix. you just exponentiate the diagonal terms...
  11. fluidistic

    QM, Heisenberg's motion equations, harmonic oscillator

    Homework Statement Hi guys, I don't really know how to solve the first part of a problem which goes like this: Consider a 1 dimensional harmonic oscillator of mass m, Hooke's constant k and angular frequency ##\omega = \sqrt{\frac{k}{m} }##. Remembering the classical solutions, solve the...
  12. fluidistic

    Need a Linear Algebra Book for Quantum Mechanics?

    I've had a proof based linear algebra course as a freshman, where I learned that the spectrum of an operator was the set of the eigenvalues of that operator. Now in quantum mechanics I learned that this isn't true and that the spectrum of an operator can contain infinitely more numbers...
  13. V

    QM: Problem with an assignment using bra and ket notation

    Homework Statement This problem is about the 1-dimensional harmonic oscillator. The normalized energy levels are labeled |n>, n=0,1,2... Two operators are given by \widehat{A} = \alpha (\widehat{a}++\widehat{a}-) \widehat{B} = i\beta (\widehat{a}+2+\widehat{a}-2) where \alpha and...
  14. Infrared

    Why is the Matrix Exponential Related to the Hamiltonian in QM?

    In class, my teacher was motivating Schrodinger's Equation, but there is one step that I do not understand or even have intuition for. I'll give the argument leading up to the step I do not understand for context. Let \hat{U}(t) be the operator that gives the wave function after time t, given...
  15. I

    Why are QM wave functions complex?

    Hi, Can anyone explain to me why the wave functions in QM must to be complex, other than to make it work when inserted into the Schrodinger equation?
  16. fluidistic

    QM, show a relation (velocity of a free particle related)

    Homework Statement Hi guys, I'm stuck at some step in a QM exercise. Here it is: Consider a free particle of mass m that moves along the x-axis (1 dimensional). Show that ##\frac{dA}{dt}=\frac{2 \hbar ^2}{m^2}\int \frac{\partial \psi}{\partial x} \frac{\partial \psi ^*}{\partial...
  17. S

    QM operator and double slit experiment doubt basics

    well i am a starter in QM, i have 2 big doubts ! let me first tell what i understood , there is phsi which defines a state of a system, phsi times x is a position operator and phsi 's derivative of x multiplied by i h is its momentum operator ... well then i operator these in phsi and what do...
  18. D

    How Do You Calculate Electron Tunneling Probability Through a Barrier?

    Homework Statement Electrons with energies of 0.201 eV are incident on a barrier 2.386 eV high and 0.383 nm wide. Find the probability for these electrons to penetrate the barrier. Homework Equations Note: h = h-bar k=Sqrt[2*m (V - E)]/h T = (1 + (V^2 (Sinh[k*L]^2))/(4*R (V -...
  19. L

    QM: Potential Energy & Particle Free Fall

    In classical mechanics is defined potential and kinetical energy for particular particle. For example, in case of free fall potential energy of the particle is ##mgh## and kinetic energy is ##\frac{m\upsilon^2}{2}##. In QM there isn't potential of the particle, but potential of part of the...
  20. fluidistic

    Calculating an integral (QM / probability)

    Homework Statement Hi guys, I've an integral that poped up in QM, it should be different from 0 (else the particle's position is known with 100% certainty while it should not with the wave function I was given). However I get 0 and I don't see where my mistake(s) is/are. ##<(x-a)^2>=\int...
  21. phosgene

    Basic QM: Probability Density w/ 3 Slits Open

    Homework Statement Suppose that we have a source of particles (e.g. photons) S, then three slits labelled 1,2 and 3, followed by a screen. For a particle that has passed through slit i, where i=1,2,3, let ψi(x) be the amplitude for the particle arriving at a position x units along the...
  22. N

    Math suggestions for learning QM

    Someone asked me which math topics to study in order to learn quantum information theory. I thought it was a good question, so here's my answer. Warning: this is off the top of my head, so it probably needs additions and/or corrections. Most of this advice applies to anyone doing quantum...
  23. S

    QM: Harmonic Oscillator wave function

    Homework Statement For the n = 1 harmonic oscillator wave function, find the probability p that, in an experiment which measures position, the particle will be found within a distance d = (mk)-1/4√ħ/2 of the origin. (Hint: Assume that the value of the integral α = ∫01/2 x2e-x2/2 dx is known...
  24. S

    Exploring the Interconnection of General Relativity and Quantum Mechanics

    I am new to this area, so pardon me if the below question might seem... 1. What area/subject/sub-topic of physics deals with attempts at bridging GR and QM? 2. What does it say? in layman language 3. What is a quantum field? 4. is there any area of QM where some credible mathematical...
  25. L

    Knowledge and understanding of QM

    In problem of infinite potential well particle can't be in a region where ##V=\infty##. How we know that in case of finite potential well that particle is in the region where ##V>E##. How we know what is energy of the particle in moment when we localize it in the region with potential ##V##...
  26. L

    QM: Coordinate & Momentum Representation w/ Fourier Transform

    Coordinate representation ##\psi=\psi(x)## Momentum representation ##\psi=\psi(p)## Fourier transform \psi(p)=\frac{1}{\sqrt{2\pi\hbar}}\int^{\infty}_{-\infty}\psi(x)e^{-\frac{ipx}{\hbar}}dx I'm confused with this ##\hbar##? Why not...
  27. Quotidian

    The Many-Worlds Interpretation of QM

    Greetings all. I'm a new poster here but have spent some time on philosophy forums previously. I subscribe to New Scientist and try and stay reasonably current with science, on the popular level at least. This week they have had a feature about physical cosmologies and 'theories of...
  28. G

    Annual survey of QM interpretations

    A long time ago, maybe 6 months, I saw an annual survey of which QM interpretation people adhered to and there was a list of maybe 10 different interpretations. I tried to find it again but couldn't. I used the advanced search tool for about 15 minutes but couldn't find anything. Does anyone...
  29. M

    Oppenheimer's QM lecture notes

    I was wondering whether Oppenheimer's legendary QM lecture notes still exist and can be found somewhere. I only found the content of theses lectures at http://bancroft.berkeley.edu/Exhibits/physics/learning03.html I assume Bohm's book ``Quantum Theory" from 1951 must contain some of the...
  30. Jim Kata

    Can Topos Theory Resolve Quantum Mechanics Paradoxes?

    I'm kind of rambling here since I'm not sure how to formulate what I'm trying to say. Is there an interpretation of quantum mechanics that uses topos theory? As in is there a way to fix some of the logical paradoxes of QM interpretations, by using a many valued logic system?
  31. B

    Another Question About Angular Momentum in QM

    Homework Statement Show that the Hamiltonian H = (p^2/2m)+V commutes with all three components of L, provided that V depends only on r.Homework Equations In previous parts of the problem, I've worked out the following relations: [L_z,x] = i\hbar y, \quad [L_z,y] = -i\hbar x, \quad [L_z, z] =...
  32. K

    The Nature of Knowledge in Quantum Mechanics

    It is ok for physics to distinguish between me and a rock out somewhere on the surface of Mars ? Who am I but a bag of chemicals ? Why would my action of observing be of any significance ? Why should the moon be "paged-in"/from-into-existence when I "observe" it and other times it is allowed...
  33. G

    What is the difference between a wave of water and qm wave?

    I get the feeling that when we say that electrons sometimes are particles or a wave depending on whether or not we measure it that what we mean by wave is not what first comes to people's mind. When we measure the electron it becomes a particle, if not then it is a wave. When I think of wave I...
  34. S

    Interference pattern calculations for unequal slits per QM theory

    I am trying to understand how QM theory (wave-functions) are applied to Interference pattern calculations for unequal slits for a single particle double slit experiment case 1: both slits are equidistant from the "center", however one slit is bigger and the ratio of the width between the slits...
  35. Logic Cloud

    Classical version of QM axioms

    Hello, I am looking for more information on the axiomatic treatment of physics. I have found some articles concerning the axioms of quantum mechanics, i.e. the Dirac-Von Neumann axioms. However, I am having a hard time finding anything on the classical version of these axioms. In these...
  36. S

    QM approximation (electron within nucleus, Griffiths 4.45b

    Homework Statement What is the probability that an electron in the ground state of hydrogen will be found inside the nucleus? a) First calculate the exact answer, assuming the wave function \psi(r,\theta,\phi) = \frac{1}{\sqrt{\pi a^3}} e^{-r/a} is correct all the way down to r=0. Let b be the...
  37. L

    Can there be molecular structures according to QM?

    In molecular orbital theory, only the electrons are considered and from that we draw conclusions about molecular shape and such. I was thinking just now, what about the nuclei? If we apply QM to the nuclei as well, wouldn't that mean that we can't know where the atoms are? or is the...
  38. B

    QM I - Decomposition of countable basic states into coherent states

    Homework Statement Consider a quantum system with a countable number of basic states \left|n\right\rangle. Calculate the decomposition into a basis of coherent states \left|λ \right\rangle all obeying \hat{a} \left|λ \right\rangle = λ \left|λ \right\rangle Homework Equations \hat{a}...
  39. L

    Quick question: Momentum operator in QM

    Homework Statement There are two ways to write the momentum operator, p = (-i hbar d/dx) and p = (hbar / i)d/dx. How do you go from one to the other? Homework Equations The two I gave above. The Attempt at a Solution I tried to see if -ih = h/i by squaring both sides, but one came out...
  40. Government$

    Is QM truly random and many world theory

    Hi everybody, i didn't wanted to create two separate threads so merged them into one. i got confused watching Brian Green explaining QM on one of his shows. He compared distribution in double slit experiments with throwing a ball on a roulette. He said that casino doesn't have to know...
  41. micromass

    Are there any physical implications of working with unbounded operators in QM?

    It is well known that unbounded operators play a crucial role in the mathematical formulation of quantum mechanics. In some sense, unbounded operators are inevitable. Indeed, we can prove that if A and B are self-adjoint operators such that [A,B]=ih, then A and B can never both be bounded. My...
  42. M

    QM Interpretation & Young's Exp: Electron Position Defined?

    According to the Copenhagen Interpretation, and considering Young's double slit experiment: Is what interferes the mathematical wave function flowing out the two slits but the electron itself takes a well defined path? Anyhow, I need a clearer idea about the position definition or...
  43. R

    [QM] Total angular momentum rotation operator

    Homework Statement How to prove that for any representation of the spin, the state e^{-i{\pi}J_x/\hbar}|j,m\rangle is proportional to |j,-m\rangle The exponential term is the rotation operator where J_x is the x-component of the total angular momentum operator, and |j,m\rangle is an...
  44. H

    What counts as an observation in QM?

    Hi I was day dreaming the other day when I realized how incomplete and vague the fundamental postulates of QM are, I mean what counts as an observation? For example simply being in the presence of a charged particle can be an observation, since (using a point particle for the sake of argument)...
  45. S

    Does QM itself prevent removal of noise without comparison

    Is there some fundamental fact of the universe (Quantum Mechanics) that prevents us from removing noise (without having to compare the entangled particles)? In the quantum eraser experiments: To get ("un-embed") the interference pattern i.e. to separate the entangled particles from the...
  46. L

    [QM] Expectation value in spin-1/2 state

    Homework Statement Basically I need to produce a state for a spin-1/2 particle such that the expectation value of <Jz> = 0 where <Jz> is for a spin-1 particle. Homework Equations Jz = (1 0 0, 0 0 0, 0 0 -1) <--[3x3] matrix The Attempt at a Solution I don't quite understand how to do this...
  47. B

    Empirical meaning of relativity in the context of QM

    In special relativity an event E is mapped to coordinates (x,t) in one inertial frame, and to coordinates (x',t') in another, and SR provides the relation between (x,t) and (x',t'). What is the empirical content of this theory (e.g. how would you operationally test it)? Since there are two...
  48. B

    How best to prepare for QM next semester.

    Greetings everyone, This is my first post although I have referenced this site numerous times. It's a great resource, so many thanks to the admin and participants. A little background: I am in my junior year of a physics/mathematics double major at an unremarkable state university. The...
  49. X

    Pick the easiest module from QM, EM or Relativity.

    The situation is messy so I'll avoid details. I absolutely must do one module this February that is listed as 'level 3' at the Open University without formally taking the prerequisites. I have to teach myself the required mathematics, in two months, to give myself a decent chance of passing. If...
  50. N

    QM: Understanding Quantization Axis for 2-Level Atoms

    Hi I have a question on how to work with quantization axis. The setup I am looking at is a single two-level atom placed at the origin (0, 0, 0), which is not perturbed by any magnetic field. I now send in a laser resonant with the transition of the atom. With a right-handed coordinate...
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