What is Quantum mechanics: Definition and 995 Discussions

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
Classical physics, the description of physics that existed before the theory of relativity and quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, while quantum mechanics explains the aspects of nature at small (atomic and subatomic) scales, for which classical mechanics is insufficient. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).
Quantum mechanics arose gradually from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. These early attempts to understand microscopic phenomena, now known as the "old quantum theory", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield.

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  1. V

    Eigenvectors of Ly and associated energies

    Homework Statement Consider a particle with angular momentum l=1. Write down the matrix representation for the operators L_x,\,L_y,\,L_z,for this particle. Let the Hamiltonian of this particle be H = aL\cdot L-gL_z,\,g>0.Find its energy values and eigenstates. At time t=0,we make a measurement...
  2. J

    B Practical applications of quantum mechanics

    What are some of the practical applications of quantum mechanics that are being utilized to optimize our existence as a species?
  3. C

    Relation between operator and experimental action

    Hi I have some questions about operator and experimental action 1, For each experimental action(no matter how trivial or complex), can they ALWAYS be described by some corresponded operator? how to proof? For example, adding some energy to excit a particle can be described in operator language...
  4. Killtech

    I A contradiction in quantum mechanics

    in an attempt to get a better understanding of what happens during a measurement i have constructed a gedanken-experiment with two photon interference that regardless of its outcome seems to contradict quantum mechanics in one way or another and i was hoping to get a clarification here where i...
  5. Y

    Potential in center of mass for Hydrogen atom

    Homework Statement A Hydrogen atom is interacting with an EM plane wave with vector potential $$\bar A(r,t)=A_0\hat e e^{i(\bar k \cdot \bar r -\omega t)} + c.c.$$ The perurbation to the Hamiltonian can be written considering the proton and electron separately as...
  6. A. Neumaier

    I Jaynes on probability in quantum theory

    This was off-topic in the thread on vacuum fluctuations where the quote appeared, so I opened a new one. I didn't know the paper before, so first need to read it...
  7. 1

    Wavefunction in a delta potential well

    Homework Statement Using the equations given, show that the wave function for a particle in the periodic delta function potential can be written in the form ##\psi (x) = C[\sin(kx) + e^{-iKa}\sin k(a-x)], \quad 0 \leq x \leq a## Homework Equations Given equations: ##\psi (x) =A\sin(kx) +...
  8. J

    I Quantum mechanics shows how the poverty of energy imposes structure....?

    From Frank Wilczek's book 'A Beautiful Question' 'Quantum mechanics shows how the poverty of energy imposes structure' P196 Is he saying the poverty of energy imposes structure in the energy of a quantum system or structure in matter? Or both? If we look at an atom it has ordered structure in...
  9. J

    Quantum Book on gauge transformations/symmetry & geometrical phases?

    Hello! I will be attending a course on condensed matter physics with emphasis on geometrical phases and I was wondering if the are any good books on gauge transformations, gauge symmetry and geometrical phases that you know of. Thanks in advance!
  10. Fetchimus

    Infinite Square Well homework problem

    Homework Statement A particle of mass m, is in an infinite square well of width L, V(x)=0 for 0<x<L, and V(x)=∞, elsewhere. At time t=0,Ψ(x,0) = C[((1+i)/2)*√(2/L)*sin(πx/L) + (1/√L)*sin(2πx/L) in, 0<x<L a) Find C b) Find Ψ(x,t) c) Find <E> as a function of t. d) Find the probability as a...
  11. jedishrfu

    A Stephen Weinberg on Understanding Quantum Mechanics

    http://www.nybooks.com/articles/2017/01/19/trouble-with-quantum-mechanics/
  12. J

    Quantum Theoretical Physics course textbooks

    Hello, I will be attending an undergraduate course called "Theoretical Physics" and I want to borrow some books from the library that cover the material of this course. I would appreciate any suggestions. The syllabus of the course is the following(I will be translating so I am sorry If...
  13. nishraptor

    Studying Want to learn Quantum Mechanics - How do I start?

    I am an engineering student with an interest in quantum mechanics : However, I really need to make a flowchart so I can understand where to proceed What I know: Math - Multivariable calculus, Differential Equations including laplace and Fourier series, and Basic Linear Algebra (Spaces...
  14. malcome123

    B What are some easy ways to show quantum mechanics

    hi I'm in grade 9 and I have to make a 20 slide slideshow and a 6 page essay or a module I need ideas on what to do
  15. Milsomonk

    I Geometric Algebra formulation of Quantum Mechanics

    Hi all, I'm reading a paragraph from "Geometric Algebra for Physicists" - Chris Doran, Anthony Lasenby. I'm quite interested in applying GA to QM but I've got to a stage where I am not following part of the chapter and am wondering if someone can shed a little light for me. The part...
  16. M

    Electron in a Coulomb Field

    Homework Statement An electron in the Coulomb Field of the proton is in the state: |ψ> = (4/5)|1, 0, 0> + (3i/5)|2, 1, 1> with |n, l, m> as the quantum numbers defining the state a) What is <E> for this state? What are <L2> and <Lz>? b) What is |ψ(t)>? Which expectation values...
  17. K

    I Unifying gravity and quantum mechanics

    I was sitting at my bed when I suddenly have an idea. The unification of electromagnetism and gravity was made with General Relativity. For this to happen, one just need to write the energy due to electromagnetic field in "differential geometry" form, through the Electromagnetic tensor, in a...
  18. astrocytosis

    Using Hund's rules to find ground state L, S, J

    Homework Statement Using Hund's rules, find the ground state L, S and J of the following atoms: (a) fluorine, (b) magnesium, and (c) titanium. Homework Equations J = L + S The Attempt at a Solution I'm having trouble understanding what L, S and J mean on a basic level. I read the textbook...
  19. almarpa

    Quantum Comparing Griffiths and Zettili for QM: Help Needed!

    Hello all! You'll see, I am self studying physics, and have already finished with Kleppner - Kolenkow mechanics (complemented with Morin) and Griffiths electrodynamics. Now I think I am prepared for QM, but I do not know which textbook is better for me. I have reduced my options to Griffiths...
  20. S

    I Understanding Coherence in Quantum Mechanics

    Hi, Can anyone please explain the physical meaning of coherence(Quantum Mechanics). Thanks is advance
  21. M

    Orthonormality of Spherical Harmonics Y_1,1 and Y_2,1

    Homework Statement Here is a copy of the pdf problem set {https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU} the problem in question is problem number 1 which asks you to prove the orthonormality of the spherical Harmonics Y_1,1 and Y_2,1. Homework Equations Y_1,1 =...
  22. M

    Solving Radial Schrodinger Equation

    Homework Statement This is a (long) multi-part question working through the various stages of solving the radial Schrodinger equation and as such it would be impractical to type it all out here but I will upload the pdf (https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU) of the...
  23. M

    Where am I going wrong in my radial equation substitution derivation?

    Homework Statement Essentially we are describing the ODE for the radial function in quantum mechanics and in the derivation a substitution of u(r) = rR(r) is made, the problem then asks you to show that {(1/r^2)(d/dr(r^2(dR/dr))) = 1/r(d^(2)u/dr^2) Homework Equations The substitution: u(r) =...
  24. Clever Penguin

    I Quantum Mechanics is not a description of reality?

    Consider a cat in a box in a room. The box also contains some radioactive isotope. A geiger counter detects if the atom decays, and if it does, it sends a signal to some sort of computer, which causes a hammer to fall and smash open a bottle of poisonous gas. So, if the atom decays, the cat is...
  25. P

    Time-Dependent Perturbation Theory

    Note this isn't actually a homework problem, I am working through my textbook making sure I understand the derivation of certain equations and have become stuck on one part of a derivation. 1. Homework Statement I am working through my text (Quantum Mechanics 2nd Edition by B.H Bransden & C.J...
  26. M

    Finding range of bound/non bound state energies of 1D finite

    Homework Statement I'm currently working on a homework set for my intermediate QM class and for some reason I keep drawing a blank as to what to do on the first problem. I'm given three potentials, V(x), the first is of the form {A+Bexp(-Cx^2)}, the others I'll leave out. I'm asked to draw the...
  27. 1

    Question about frequency of light

    I flicker an LED on and off at a rate on the order of hundreds of kHz. The light, even though it is sent in pulses, still has its own frequency, correct? The frequency at which I turn the light on and off is not related to the frequency of the photons. Is this correct?
  28. D

    Expectation values of the quantum harmonic oscillator

    Homework Statement Show the mean position and momentum of a particle in a QHO in the state ψγ to be: <x> = sqrt(2ħ/mω) Re(γ) <p> = sqrt (2ħmω) Im(γ) Homework Equations ##\psi_{\gamma} (x) = Dexp((-\frac{mw(x-<x>)^2}{2\hbar})+\frac{i<p>(x-<x>)}{ħ})##The Attempt at a Solution I put ψγ into...
  29. P

    Normalization of the Angular Momentum Ladder Operator

    Homework Statement Obtain the matrix representation of the ladder operators ##J_{\pm}##. Homework Equations Remark that ##J_{\pm} | jm \rangle = N_{\pm}| jm \pm 1 \rangle## The Attempt at a Solution [/B] The textbook states ##|N_{\pm}|^2=\langle jm | J_{\pm}^\dagger J_{\pm} | jm \rangle##...
  30. TheSodesa

    A gyromagentic ratio for a cylinder

    Homework Statement In classical physics, a system's magnetic moment can be written like so: \mu = g\frac{Q}{2M}L, where ##Q## is the total charge, ##M## is the total mass of the system and ##L## the angular momentum. a) Show, that for a cylinder (##I = \frac{1}{2}MR^2##) spinning around its...
  31. Eureka99

    Sources for quantum mechanics?

    Hi everyone, I wanted to know if any of you knows very good sources for quantum mechanics and spectroscopy fundamentals, like greats books, youtube videos (lectures), or any other option. I' m studying spectroscopy at the moment, and last year I've done the Physical Chemistry II course ( quantum...
  32. C

    Measurement standard for joules = Momentum in kilograms

    Basically, I found the energy of a photon using its frequency ((6.8*10^15) and E=(3.6496394*10^-16)) and so I then used "p=E/c" to find the momentum and got 1.2173887*10^-24 however I don't know the measurement of the momentum. Is there a better equation to use to find momentum, and what would...
  33. S

    A Adiabatic process - quantum mechanics and thermodynamics

    A diabatic process is defined as follows: Rapidly changing conditions prevent the system from adapting its configuration during the process, hence the spatial probability density remains unchanged. Typically there is no eigenstate of the final Hamiltonian with the same functional form as the...
  34. Avimanyu Ray

    Quantum Starting books for Quantum Mechanics

    Hello I'm an undergrad. Can anyone suggest me books, articles, lectures for studying quantum mechanics as a fresh starter? I tried r. Shankar but it only mathematical to me, couldn't get the physical significance. On the other hand, Griffith got way deep in concepts without sufficient examples...
  35. VonNathan

    I Could somebody tell me good book about degenerate matter ?

    Could somebody tell me good book about degenerate matter ?
  36. 1

    Help normalizing a wave function

    Homework Statement I don't see how the author normalizes ##u(r)=Asin(kr)##. From Griffiths, Introduction to Quantum Mechanics, 2nd edition, page 141-142: http://imgur.com/a/bo8v6 Homework Equations ##\int_0^{\infty} \int_0^{\pi} \int_0^{2\pi}|A|^2 \sin^2(\frac{n\pi r}{a})r^2 \sin \theta...
  37. redtree

    A Conjugate variables in the Fourier and Legendre transforms

    In quantum mechanics, position ##\textbf{r}## and momentum ##\textbf{p}## are conjugate variables given their relationship via the Fourier transform. In transforming via the Legendre transform between Lagrangian and Hamiltonian mechanics, where ##f^*(\textbf{x}^*)=\sup[\langle \textbf{x}...
  38. A. Neumaier

    Insights The Vacuum Fluctuation Myth - Comments

    A. Neumaier submitted a new PF Insights post The Vacuum Fluctuation Myth Continue reading the Original PF Insights Post.
  39. TheSodesa

    The width of a finite potential well

    Homework Statement An electron is enclosed in a potential well, whose walls are ##V_0 = 8.0eV## high. If the energy of the ground state is ##E = 0.50eV##, approximate the width of the well. Answer: ##0.72nm## Homework Equations For an electron in a potential well, whose energy is less than...
  40. TheSodesa

    A relativistic electron in a potential box

    Homework Statement In a potential box (##L = 1.00pm##) an electron moves at a relativistic speed, meaning it's momentum can't be expressed as ##P = \sqrt{2mE}##. a) Using the uncertainty principle, show that the speed is indeed relativistic b) Derive an expression for the allowed energy states...
  41. J

    I Hartree Fock v.s. Configuration Interaction

    Hey everyone, For my studies I have to read a part about approximation methods in Quantum Mechanics. Unfortunately I'm having difficulties understanding some concepts. If I'm correct, for describing a multi fermionic system of n electrons, the Hartree Fock (HF) method uses a Slater determinant...
  42. M

    Setting up an Uncertainty Problem

    Homework Statement A proton is known to lie within the nucleus of a gold atom. The radius of a gold nucleus is approximately 6 fm. What is the minimum uncertainty in the proton’s velocity [you may treat the problem as one-dimensional and you should express your answer as a fraction of c]...
  43. P

    Momentum and Position Operator Commutator Levi Civita Form

    Homework Statement Prove that ##[L_i,x_j]=i\hbar \epsilon_{ijk}x_k \quad (i, j, k = 1, 2, 3)## where ##L_1=L_x##, ##L_2=L_y## and ##L_3=L_z## and ##x_1=x##, ##x_2=y## and ##x_3=z##. Homework Equations There aren't any given except those in the problem, however I assume we use...
  44. amjad-sh

    Studying Self-studying quantum mechanics

    Hello. I'm studying quantum mechanics by my own. I'm targeting to be a condensed matter physicist. What is the best way to grasp the concepts as fast as possible,and what should I do to become a good physicist in the near future? Thanks. Note: I've got a bachelor degree in physics but I stopped...
  45. weezy

    I Bohr-Sommerfield quantization of motion

    From wikipedia I understand that the old quantum condition $$\oint_{H(p,q)=E} p_i dq_i = n_i h $$ states that not all kinds of motion are permitted in a system. My question is why is this called the old quantum condition and what is quantization of motion? Does this mean that a particle jumps...
  46. A

    B Quantum field theory VS Quantum mechanics

    Hello I am little bit confused about one topic on theoretical Physics and that is If we want to describe our Quantum world (example atoms in metal) then should I use Quantum field theory or Quantum mechanics?
  47. G

    What Colors of Light Are Absorbed by Electrons in a 3.1 nm Infinite Well?

    Homework Statement Determine what colors of visible light would be absorbed by electrons in an infinite well, N = 3.1 nm. The effective mass for an electron in GaAs is one-fifteenth of the standard electron mass. Homework Equations En = πh2/[2*N2*me/15]*n2 L = nλ/2 Ψ = √(2/L)sin(nπx/L) The...
  48. I

    I Mass Defect: Exploring the Possibilities of Quantum Mechanics

    I've just watched a video by PBS spacetime on how an object with more potential energy has more mass, or less, in some cases (mass defect). But there is a problem. Quantum mechanics tells us that a particle has a chance of appearing at difderent places ( wave function), and that it also...
  49. J

    B Double Slit detectors question

    My question about the double slit experiment is this: why is it that nobody suspects that the detectors used to detect particles as they pass through the slits in the double slit experiment aren't causing some interference with the experiment which makes it seem as though they are acting like...
  50. TLeit

    Courses Quantum Mechanics Math Course

    Sorry I keep posting about this. I had settled on Probability (Probability in discrete and continuous sample spaces; conditional probability; counting techniques; probability functions; binomial, Poisson, normal distributions; and transformations of variables.) based off of previous answers to...
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