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. renec112

    Harmonic oscillator - chance of of finding particle x>0

    Homework Statement A particle is moving in a 1-dimensional harmonic osciallator with the hamiltion: ## H = \hbar \omega (a_+ a_- + \frac{1}{2})## at time ## t=0## the normalized wave function is given by ## \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x) + i\psi_1(x)) ## Task: Calculate for ## t \geq...
  2. renec112

    QM: expectation value and variance of harmonic oscillator

    Homework Statement A particle is moving in a one-dimensional harmonic oscillator, described by the Hamilton operator: H = \hbar \omega (a_+ a_- + \frac{1}{2}) at t = 0 we have \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x)+i\psi_1(x)) Find the expectation value and variance of harmonic oscillator...
  3. amjad-sh

    A What is inversion symmetry in solids and why does it break at the surface?

    Hello Can somebody explain for me what is the meaning of inversion symmetry in solids? and why does it breaks at the surface? and also why this inversion symmetry breaking leads to SOC(spin orbit coupling)? If somebody also know a document that explain this in full details(from A to Z) please...
  4. R

    Working with X and P operators in QM

    Homework Statement Consider the eigenstates of a particle in an infinite well with walls at ##x=\pm a##. without explicitly evaluating any integrals, what is the expectation value of the following operator $$\hat{x}^2\hat{p_x}^3+3\hat{x}\hat{p_x}^3\hat{x}+\hat{p_x}^3\hat{x}^2$$ Homework...
  5. S

    Griffith's QM, Harmonic Oscillator approximate solution eq

    Homework Statement on page 51 (of my book, probably not current) section 2.3.2 equation 2.74 and 2.75 d2ψ / dξ2 ≈ ψξ2 Homework Equations This is an approximation of the Schrodinger equation with a variable introduced ξ = √(mω/h) The solution is given: ψ(ξ) = Ae-ξ2/2 +Beξ2/2The Attempt at...
  6. ISamson

    B Massive Space Objects Have Connections to QM Math

    Massive Space Structures Have Surprising Connection to Quantum Mechanics Math Reading my daily science news I came across an interesting article that talks about how massive space objects have unexpected relationships to quantum mechanical mathematics. I was quite surprised to hear this, as I...
  7. dRic2

    I How small does a system have to be for QM to be necessary?

    If we are talking bout a single atom QM is obviously necessary, but when we are talking about a bunch of molecules (like gases/fluids) statistical mechanics works fine too. I remember it has something to do with ##\hbar## but I don't remember much and I can not quantify it. Thanks
  8. Zaya Bell

    I Complex Numbers in Wave Function: QM Explained

    I just need to know. Why exactly what's the complex number i=√–1 put in the wave function for matter. Couldn't it have just been exp(kx–wt)?
  9. SemM

    A What are some recommended books on non-standard quantum mechanical models?

    By fresh42's invitation, I here attach a paper which is related to the post on non-standard qm-models https://arxiv.org/pdf/cond-mat/9705290
  10. SemM

    A Can Quantum Mechanics be Studied in Banach Spaces or Other Non-Hilbert Spaces?

    Hi, are there any models known in QM where the wavefunctions do not have to be infinitely differentiable, and thus can exist in other spaces than the Hilbert space? I assume Banach spaces allow elements that are not infinitely differentiable as subsets. Can therefore certain phenomena in QM be...
  11. VIctor Medvil

    A I want to know the exact problems of Merging GR and QM

    This thread is I want a set of experts in the subject to show me the exact math of why Einstein's field Equations along with Special Relativity and Schrodinger's Equation along with deeper QM like QFT cannot be fused with GR. I want to see the exact anomalies in the equations myself from the...
  12. W

    How Does a Phase Shift Affect the Mach-Zehnder Interferometer?

    Homework Statement Hi all, I'm working on the following problem and would like some help. Many thanks in advance! The Figure below presents the Mach-Zehnder interferometer with an additional phase shift element in the upper path. $$\left( \begin{array}{cc} e^{i\phi} & 0 \\ 0 & 1 \end{array}...
  13. M

    QM: Writing time evolution as sum over energy eigenstates

    Suppose I have a 1-D harmonic oscilator with angular velocity ##\omega## and eigenstates ##|j>## and let the state at ##t=0## be given by ##|\Psi(0)>##. We write ##\Psi(t) = \hat{U}(t)\Psi(0)##. Write ##\hat{U}(t)## as sum over energy eigenstates. I've previously shown that ##\hat{H} = \sum_j...
  14. F

    I Thought experiment about wave functions

    Suppose we have a particle, let's say an electron, in a box of size D. And we add another one next to it at some distance L center to center. How do we solve for the wavefunctions of the electron. Can it be solved in normal QM or do we need QFT. Thanks.
  15. LarryS

    I Why is position-space favored in QM?

    In non-relativistic QM, when one speaks of a "wave function" it is understood that one is referring to the position-space version of the wave function. Even if the observable being measured is other than position, like momentum or energy, the associated eigenfunctions are always from the...
  16. SemM

    I How to identify admissible functions in QM by simple math?

    Hi, in QM literature the inadmissible solutions to the Schrödinger eqn are often , if not always, quoted in the text as "inadmissible", because they are discontinuous, not-single valued, not square integrable and not infinitely differentiable. However in a discussion with Dr Du yesterday...
  17. SemM

    I Exploring the Equivalence of Different Representations in Quantum Mechanics

    Hi, I found this article very interesting, given the loads of question I have posted in this regard in the last months. I cannot recall where I got the link from, and if it came from Bill Hobba in some discussion, thanks Bill! If not, thanks anyway for your answers and contributions. Here is...
  18. pellis

    A Who wrote "Ch 6 Groups & Representations in QM"?

    Who really wrote the best introductory account of representation theory in QM that I've seen so far ? [Likely mis-attribution discussed here below; prefixed "Advanced" to reach lecturers who are more likely to know the answer to this question.] It's available via...
  19. A

    Why is the expectation value of the commutator not zero in method 1?

    I'm trying to extract the expected value of a |+45> polarized photon in the HV- base. I do it in two ways, one is correct and the other I get wrong answer. What am I doing wrong in the first method that is wrong? method 1 method 2 thanks in advance
  20. LarryS

    I Eigenvectors - eigenvalues mappings in QM

    In non-relativistic QM, say we are given some observable M and some wave function Ψ. For each unique eigenvalue of M there is at least one corresponding eigenvector. Actually, there can be a multiple (subspace) eigenvectors corresponding to the one eigenvalue. But if we are given a set of...
  21. F

    I Momentum Entanglement: The Technicalities and Usage in Electron Experiments

    In the original EPR paper momentum was giving as an example of entanglement, but I don't see that discussed by any thread or papers for that matter, why is that. What is the technicalities of this entanglement for two electrons for example, is it also instantaneous and why is it not used to...
  22. W

    QM: Probability of measuring momentum

    Hi all, My question is in reference to the following paper: https://arxiv.org/pdf/1202.1783.pdf In equation 3.8, the author computes an order-of-magnitude approximation of probability of measuring negative momentum from the following wavefunction: $$ \Psi_k =\sum_{k=1,2}...
  23. DrClaude

    Quantum Modern QM by Sakurai and Napolitano

    I have recently received an inspection copy of the 2nd edition of Modern Quantum Mechanics by Sakurai, now co-authored by Jim Napolitano. Here goes some free publicity: I love this book! It is like the old Sakurai, simply better. I know that many here at PF recommend Sakurai for advanced...
  24. T

    Finding eigenvector QM 2x2 matrix

    Homework Statement I am having a issue with how my lecture has normalised the energy state in this question. I will post my working and I will print screen his solution to the given question below, we have the same answer but I am unsure to why he has used the ratio method. Q4. a), b), c)...
  25. T

    Intro to probability density QM

    Homework Statement Q: A particle is in a linear superposition of two states with energies: ##E_0##& ##E_1## $$|\phi>=A|E_0>+\frac{A}{\sqrt{3-\epsilon}}|E_1>$$ (a) What is the value of A ? Express your answer as a function of ##\epsilon## (b) Use your expression to plot A vs ##\epsilon## (c)...
  26. L

    Books for overview of QM and/or QFT?

    I am not ready to learn the formalism for QM or QFT (maybe someday). Does anyone have any book suggestions for a beginner like myself that present the theories in accurate ways without going into all the mathematical formalism? Preferably something that is not tied to one interpretation of the...
  27. bhobba

    I Einstein's View of Quantum Mechanics

    Hi All This is an outgrowth of the following thread: https://www.physicsforums.com/threads/light-photons-waves-particles-wave-particle-duality.934063/ OK first we need to clear up a few misconceptions about Einsteins view of QM. It is often said Einstein didn't believe in QM. That's really a...
  28. MichPod

    I Self education: how to proceed from QM to QFT?

    I tried to start many books/video courses to learn QFT but this failed because of many factors, including my weak math/physics background, laziness, lack of time, lack of persistence, just to count some. The whole blame is on me, no doubt. Still, if I was able to learn QM to some extent...
  29. tarkin

    QM harmonic oscillator - integrating over a gaussian?

    Homework Statement [/B] For the first excited state of a Q.H.O., what is the probability of finding the particle in -0.2 < x < 0.2 Homework Equations Wavefunction for first excited state: Ψ= (√2) y e-y2/2 where: The Attempt at a Solution To find the probability, I tried the integral of...
  30. K

    A Osterwalder-Schrader theorem and non-relativistic QM

    I have recently learned a bit about the Osterwalder-Schrader theorem. From my understanding, this tells you when a Euclidean path integral can be analytically continued to a valid relativistic Hermitian quantum field theory (one needs reflection positivity etc.). I am curious about...
  31. Jianphys17

    Is understanding analytical mechanics essential for studying QM?

    Hi at all. I'm wondered is necessary learn well analytical mechanic ( eg learning The Goldstein's book), for understand and study QM ?
  32. C

    A What are local and non-local operators in QM?

    In Hartree-Fock method, I saw the Fock operator has two integrals: Coulomb integral and exchange integral. One can define two operator. "The exchange operator is no local operator" why? Whats de diference: local and no local operator? And why do the operators have singularities? thanks
  33. M

    QM: Solving Free Particle with 3D Wave Function Using Fourier Transform

    Homework Statement Hi, i have this problem: In a 3D space, a free particle is described by : $$ \Psi = Ne^{-ar} $$ with $$ r=| \vec r | $$ at the time t=0 . How can we write the wave function whit $$ \hbar \vec k $$ ?Homework EquationsThe Attempt at a Solution I know how to resolve this...
  34. RJLiberator

    QM: 1D Potential Well Spring - Energy Levels

    Homework Statement 1D Potential V(x) = mw^2x^2/2, part of a harmonic oscillator. Suppose that the spring can only be stretched, so that the potential becomes V=infinity for x<0. What are the energy levels of this system? Homework EquationsThe Attempt at a Solution I argued my way though this...
  35. A

    High Energy Recommended books in HEP, QFT, QM, GR

    Hi everyone! I'm trying to make a list of recommended books (introductory and advanced). So far, what I was able to search are the following: Particle Physics: - Griffiths: Introduction to Elementary Particles - Thomson: Modern Particle Physics - Nachtmann: Elementary Particle Physics -...
  36. A

    QM: Purity, two-outcome measurements

    Homework Statement Homework Equations in addition to those provided in the questions, I used the following: Tr(B) = sigma<x_j|B|x_j> purity = Tr(rho^2) The Attempt at a Solution [/B] I find calculating trace and purity very confusing. Am I on the right track with question 1? With...
  37. Dadface

    I QM Assumptions Regarding Entanglement Properties

    In a nutshell I think that in local realistic theories it is assumed that: Each entangled object has definite properties at all times, even when not observed. I know the assumption is proved to be incorrect but is that an assumption actually made in such theories?But what assumptions about...
  38. W

    I Probability of Staying in x<0 for Superposition of 2 Gaussians

    Homework Statement I am supposed to find probability of staying in x < 0 for a superposition of two Gaussians. The wavefunction is something along the lines of: Homework EquationsThe Attempt at a Solution Usually, the step involved in finding probabilities for 1 particle is just to perform...
  39. T

    Do many people believe in false QM ideas

    When I first started QM i found all sorts of wild ideas on the internet, such as consciousness affects the experiment and the universe needs observers to exist. The articles also somehow misrepresent experiments such as the double slit experiment and the delayed choice experiments to claim that...
  40. W

    QM: Difference between these Initial Wavefunctions

    Homework Statement I've been asked as a part of some school project to find the Fourier transform, and time evolution of the following initial wavefunctions: 1. ##\Psi(x,0) = Ae^{\frac{-x^2}{2\sigma ^2}}## 2. ##\Psi(x,0) = Be^{\frac{-x^2}{2\sigma ^2}}e^{\frac{ipx}{\hbar}}## What physical...
  41. zonde

    B Dual meaning of "measurement" in QM

    Reading about collapse and Born rule it gives strong feeling that there is semantic mess in QM with the word "measurement". Wikipedia describes Born rule in following way: In its simplest form it states that the probability density of finding the particle at a given point is proportional to the...
  42. entropy1

    I Has Quantum Mechanics Solved the Measurement Problem?

    Is the measurement problem in QM addressed and solved by now? If not, can we speak of QM as a description of reality? Given the statistical nature of QM, can we say it predicts reality? What is it that QM addresses?
  43. zonde

    I Binding energy in QM and in GR

    I would like to ask rather general question. Can a binding energy of some QM process at the same time be binding energy of gravity? I am just trying to find overlap between QM and GR and I have thought about this question but I'm not sure how to tackle it.
  44. T

    Griffith Intro to QM, 1st order perturb theory in time-dep

    Homework Statement ca(0)=1, cb(0)=0 zeroth: ca(t)=1, cb(t)=0 1st: ca(t)=1, cb(t)=i/hbar*integral(H'(t) exp(iwt)) dt ca^2+cb^2=1 to 1st order of H'.: What does it mean? it is evidently not 1 at all. Homework EquationsThe Attempt at a Solution
  45. P

    I How are degrees of freedom understood in QM?

    I'm having a hard time understanding 'degrees of freedom'. Could someone please provide an example in terms of Quantum Mechanics about what a 'degree of freedom' could be represented as? Is it simply a number of observations of a physical system to determine the arrangement of particles within...
  46. F

    B Is there a tension between QM and QFT?

    There seems to be some -at least- conceptual difference between particles in QFT which is just a point -eventually- in the field AND the particle in QM which is described by a wavefunction which is extended in space. As if QFT somehow "collapses" the wavefunction.
  47. W

    I Can Bound States Leak and How Do Scattering States Behave?

    Hi all, I'd like some assistance regarding some issues I have understanding such states. (Referencing Griffiths' QM) 1) Meaning of Bound and Scattering States. The bound states I have studied thus far are limited to the infinite square well and the quantum harmonic oscillator. In the case of a...
  48. RJLiberator

    QM: Potential, Finite Step Function

    Homework Statement A beam of particles of mass m and energy E is incident from the right unto a square well potential given by ##V(x)=-V_0## for ##-a<x<0##, and ##V(x)=0## otherwise. Solve the Schrodinger equation to determine the wave function which describes this situation. Determine the...
  49. W

    I Questions Regarding Free Particles - Griffith's QM (I)

    Homework Statement [/B] 1) I don't quite understand what 2.94 means on its own. It was derived from 2.93, yet it doesn't show a superposition of any sort. The author then takes 2.94, and attempts to normalise it by stating ##\int \Psi_k^* \Psi_k dx = \mid A^2 \mid\int dx = \infty ## What...
  50. A

    I Exact value for every observable in QM?

    Folks - I'm asking a lot of questions lately (hopefully useful not just for me). By chance, reading about quantum states, I referenced Wikipedia (dubious I know), and came across the following phrase (with a citation, that I will check): "Even in quantum theory, however, for every observable...
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