Quantum mechanics Definition and 994 Threads

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. jk22

    Error : what is n in quantum mechanics

    Suppose I have an operator A. Its average is <A> and the standard deviation $$\sigma=\sqrt {<A^2>-<A>^2} $$. I now want the standard error which is $$\sigma/\sqrt {n} $$. I wondered what n is in quantum mechanics ? The wsvefunction is supposed to describe a single particle so it should be 1 ...
  2. M

    Entangled Photons: What Happens to Photon B? Can Two Combine?

    If a photon A is entangled with photon B and one somehow destroys photon A, what will happen to photon B? Will it also get destroyed? And can two entangled photons combine into one?
  3. Clarence Liu

    Using Mathematica to solve for Jacobi Identity

    Hi everyone, I'm new to Physics Forums and to Mathematica, as well as Jacobi Identity. In any case, I was wondering on how I may use Mathematica to solve various Quantum Mechanics related problems through commutators. Like if it's possible to find out what is the form of a particular commutator...
  4. phys-student

    Introductory quantum mechanics problem

    Homework Statement Consider A(x) is an arbitrary function of x, and px is the momentum operator. Show that they satisfy the following condition: [px,A(x)] = (-i/ħ)*d/dx(A(x)) where [px,A(x)] = pxA(x) - A(x)px Homework Equations ħ = h/2π px = (-iħ)d/dx The Attempt at a Solution Starting with...
  5. RGalbiati

    Quantum Quantum mechanics (mathematics): exercise book

    Hi everybody I'm currently looking for an introductory quantum mechanics book which emphasizes the mathematical aspects of it. I especially need exercises in order to pass a written exam, but I'd like to have even lots of examples. I've already gone through the whole "Picasso" (it's an italian...
  6. G

    Zettili QM Problem on Trace of an Operator

    Homework Statement In Zettili's QM textbook, we are asked to find the trace of an operator |\psi><\chi| . Where the kets |\psi> and |\chi> are equal to some (irrelevant, for the purposes of this question) linear combinations of two orthonormal basis kets. Homework Equations...
  7. P

    Quantum Tunneling of a conduction electron in Copper

    Homework Statement A conduction electron moves through a block of Cu until it reaches the surface. At the surface the electron feels a strong force exerted by the nonuniform charge distribution in that region. This force tends to attract the electron back into the metal which is what causes the...
  8. J

    Why does a black body radiate in all the frequency spectrum?

    I understand why a black body absorbs every frequency(it is the definition of a black body!) but i do not understand why it also radiates at all frequency spectrum.
  9. J

    Black Body radiation and thermal equilibrium

    Wikipedia writes: "Black-body radiation is the type of electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment". Why does it write "thermodynamic equilibrium"? If it is not in a thermodynamic equilibrium, then what changes as far as the absorption...
  10. Suman Saha

    Quantum Quantum Mechanics Book: Reference Guide w/Theory & Examples

    Suggest for a reference book for quantum mechanics having detailed theoretical explanation and lot of solved examples.
  11. Q

    Tannor Quantum Mechanics derivative of variance of position

    0http://stackoverflow.com/questions/34833391/tannor-quantum-mechanics-derivative-of-variance-of-position# In the Tannor textbook Introduction to Quantum Mechanics, there is a second derivative of chi on p37. It looks like this: χ"(t) = d/dt ( (1/m) * (<qp + pq> - 2<p><q> ) (Equation...
  12. P

    How do electromagnetic waves transfer energy?

    I was thinking about a laser, a very strong laser, how does it "burn" things? And what about the microwave oven? What happens in the atomic scale? I know that when something has an increase in temperature the atoms moves quicky because the the temperature is proportional to the kinetic energy...
  13. PhysicsKid0123

    Measurement-Free Interactions (MFI)

    So I have not been able to find too much information about this. Specifically in the context of the double slit experiment. I've seen just about the only video on Youtube that tries to explain this, but I did not understand-- I felt like somethings were not explained. I am acquainted with why a...
  14. J

    What kind of differential equations one must know for QM?

    I will be taking a first course on Quantum Mechanics and just wanted to know what kind of ordinary differential equations must i know before going into the course. Thank you!
  15. T

    Average momentum of energy eigenstates is always zero?

    Look at the following derivation: ## p=\frac{im}{\hbar}[H,r] ## if ##H|\psi\rangle=E|\psi\rangle##, then ## \langle \psi|p|\psi \rangle = \frac{im}{\hbar}\langle \psi|Hr-rH|\psi \rangle = \frac{im}{\hbar}\langle \psi|r|\psi \rangle(E-E)=0 ## What's wrong with my derivation or it is true that...
  16. J

    From Classical to Quantum Mechanics

    What parts of Classical Mechanics must someone know before studying Quantum Mechanics in order to understand the former in all its glory? Thank you
  17. N

    If im not measuring its not there?

    Without getting too deep into the physics or philosophy of quantum mechanics, and I'm NOT talking about theory (no 'what the equations say') but if I'm not looking at my couch does that it mean at the moment it doesn't exist? Or if I'm not looking at my dad he isn't there but in the form of a wave?
  18. zonde

    Quantum mechanics is not weird (locality and non-locality weirdness)

    Let's be fair, it's not true. Pure states are the ones that correspond to exact physical states. And it is not intuitive that exact physical states should transform continuously. Our belief about outcome can transform continuously but belief does not correspond to pure state.
  19. A

    Quantum Mechanics Simulations - Project

    Hello. I am not too sure if this thread is the right place to post this in. But anyway. I have to make a project for my final year, and I have chosen to make a quantum mechanics based project. I am thinking of doing some quantum mechanics based simulations, give a little bit of history of...
  20. A. Neumaier

    I Quantum mechanics is not weird, unless presented as such

    Does quantum mechanics have to be weird? It sells much better to the general public if it is presented that way, and there is a long history of proceeding that way. But in fact it is an obstacle for everyone who wants to truly understand quantum mechanics, and to physics students who have to...
  21. Andreol263

    Quantum Modern Quantum Mechanics Sakurai

    What I'm going to need to learn from this book? I'm going to need read something before?
  22. S

    'Symmetry argument' for eigenstate superposition

    Homework Statement For an infinite potential well of length [0 ; L], I am asked to write the following function ##\Psi## (at t=0) as a superposition of eigenstates (##\psi_n##): $$\Psi (x, t=0)=Ax(L-x) $$ for ## 0<x<L##, and ##0## everywhere else. The attempt at a solution I have first...
  23. Kiarash

    Fermi's Golden Rule: Countable Quantum States & H-Theorem

    Consider a system with countable quantum states. One can define Jij as the rate of transition of probability from i-th to j-th quantum state. In H-theorem, if one assumes both $$ H:=\Sigma_{i} p_{i}log(p_{i})$$ $$J_{ij}=J_{ji}$$ then they can prove the H always decrease. The latter is Fermi's...
  24. G

    Quantum mechanics and mathematical physics textbooks

    Hello!can someone propose a good textbook for quantum mechanics and mathematical physics(including green function)?I would like to buy those books so i want something which is one of the best to have in your libraby!
  25. weezy

    How is the uncertainty relation preserved in this experiment

    For an electron can I not do the following to determine both the position and momentum? I take a screen with a small hole and I eventually make the hole smaller and smaller. Cathode rays emitted will hence get diffracted after passing through the hole making momentum more and more uncertain...
  26. nmsurobert

    Quantum Mechanics 1: Should I Take It Despite Receiving a D?

    I took quantum mechanics 1 this semester. It's part one of two that I need to graduate. I received a D in the course. I'm not sure if the D prohibits me from taking quantum 2 next semester. I'm still waiting to hear back from my advisor. The course catalog doesn't say that a C or better is...
  27. S

    How to Derive Raising and Lowering Operators from Ladder Operator Definitions?

    Homework Statement Define n=(x + iy)/(2)½L and ñ=(x - iy)/(2)½L. Also, ∂n = L(∂x - i ∂y)/(2)½ and ∂ñ = L(∂x + i ∂y)/(2)½. with ∂n=∂/∂n, ∂x=∂/∂x, ∂y=∂/∂y, and L being the magnetic length. Show that a=(1/2)ñ+∂n and a†=(1/2)n -∂ñ a and a† are the lowering and raising operators of quantum...
  28. S

    Linear Harmonic Oscillator Quantum Mechanics

    Homework Statement A linear harmonic oscillator with frequency ω = hbar / M is at time t = 0 in the state described by the wave-function: Ψ(x,0) = C( 1 + √2x) e-x2/2 Determine the values of energy which can be measured in this state. I'm not really sure where to start this question and was...
  29. AlexGLSY

    Exploring the Probabilistic Nature of Quantum Mechanics

    Why is Quantum mechanics probabilistic? what prevents it from being deterministic, like classical mechanics ?(is it the lack of information about the processes and the forces applied at this scale?)
  30. E

    Ground-state energy of harmonic oscillator(operator method)

    I studied this from Griffith Chapter 2, with the algebraic (raising and lowering operator) method, we reached the ground state by setting a_Ψ0 = 0 , then we got what the ground state is, and then plugged it in the Schrodinger equation to know the energy, and it turned out to be 0.5 ħω. My...
  31. Scott Hill

    Teaching advanced quantum mechanics

    I'm teaching advanced undergraduate quantum mechanics in the spring for the first time, using Griffiths' Introduction to Quantum Mechanics. (It's basically "mathematical methods of quantum mechanics: eigenstates, bra-ket notation, ladder operators, WKB approximation, etc). If you've taken or...
  32. W

    What is the Exponential Function in Quantum Mechanics?

    Homework Statement The question is here. http://postimg.org/image/l7aw07sr9/ Homework EquationsThe Attempt at a Solution I don't even understand what it's asking because how can a stationary state be an exponential function with no boundaries? I would appreciate any insight, thank you.
  33. B

    Time in Relativity & Quantum Mechanics: A Philosophical Perspective

    this question is a bit philosophical... in general relativity time "doesn't exist", and all of spacetime is already a preexisting pseudo riemannian manifold. however experiments have only shown time run at different rates, not that spacetime is preexisting. in our ordinary experience time is...
  34. S

    Unitary and linear operator in quantum mechanics

    Given a transformation ##U## such that ##|\psi'>=U|\psi>##, the invariance ##<\psi'|\psi'>=<\psi|\psi>## of the scalar product under the transformation ##U## means that ##U## is either linear and unitary, or antilinear and antiunitary. How do I prove this? ##<\psi'|\psi'>## ##= <U\psi|U\psi>##...
  35. E

    Trace Distance in quantum mechanics

    Hi, I am trying to familiarize myself with the quantum mechanical trace distance and hit a brick wall. Thus, I would appreciate your help with the matter! I am reading up on trace distance using Nielsen, Chunang - Quantum Computation and Quantum Information and Bengtsson, Zyczkowski - Geometry...
  36. J

    Applied Any books on Ordinary Differential Equations w/ applications

    Hello, I really need a good book on ordinary differential equations with applications on Quantum Mechanics, as I will be attending a course on QM but I do not have the proper mathematical background that is needed.
  37. M

    Time Independent Schrodinger Equation

    Homework Statement Verify that a plane wave ψ(x) = Ae-ikx is a solution to the time independent Schrodinger equation for a free particle in one dimension. Can it be normalised? Why?[/B]Homework EquationsThe Attempt at a Solution My lecturer's notes are all over the place, which is frustrating...
  38. DeldotB

    Neutrino Oscillation: Solving for x,t

    Homework Statement Suppose that two neutrinos are created in the sun - call the states |{ \nu_1}\rangle and |{ \nu_2}\rangle . (Among many other things) I am asked to show that once the neutrinos have propigated a distance x after a time t, the states satisfy: |{ \nu_1}(x,t)\rangle =...
  39. entropy1

    Self-Study Quantum Mechanics: Can I Do It w/ Poor Math Skills?

    Whole my life I have been interested in Quantum Physics. I have a bachelor degree in IT. I did not finish my studies. I have always been quite sloppy in studying in school. As a result, my mathematics skills are terrible. I often get pointed out on this forum that I better start with the...
  40. S

    Electron Spin Problem: Exploring the Stern-Gerlach Experiment

    Hello, I've been reading the Stern-Gerlach experiment, and where the concept of electron spin is introduced, am facing a problem, i.e., if you consider electron a charged rotating sphere, then the electromagnetic energy and size of the electron becomes huge! So how do you deal with this? Thanks...
  41. B

    Spin 1/2 systemin Sakurai quantum mechanics

    Homework Statement Homework Equations This is a passage from Modern Quantum Mechanics by Sakurai ( page 26~27) The Attempt at a Solution I wonder how i can get 1.4.8 , 1.4.9 equations . and what do they mean?
  42. S

    Particle in a well potential/energy continuity

    Hello again, Am facing a difficulty, the question is that , Is energy and momentum conserved for a particle in an infinite square well, at the boundary i.e, at x=a, where the potential suffers an infinite discontinuity?? V=0 for -a<=x<=a V=infinite else-where Thanks in...
  43. B

    How to prepare for the Quantum Mechanics course?

    Dear Physics Forum personnel, I am a college student with double majors in the mathematics and computer science. I recently got interested to the art of quantum mechanics course through my current undergraduate research in the theoretical computer science, where my near-future project will...
  44. P

    Find the energy levels of a spin s = 3/2 particle

    Homework Statement Find the energy levels of a spin ##s=\frac{3}{2}## particle whose Hamiltonian is given by: ##\hat{H}=\frac{a_1}{\hbar^2}(\hat{S}^2-\hat{S}_x^2-\hat{S}_y^2)-\frac{a_2}{\hbar}\hat{S}_z## where ##a_1## and ##a_2## are constants. Homework Equations In the ##\hat{S}_z## basis...
  45. quantum.cmptr

    What Are Some Trustable Websites about Quantum Mechanics?

    What are some reputable, trustable websites that explain quantum mechanics and all its concepts well? Also, what are some good books about quantum mechanics? (Note: This is for the general ideas of quantum mechanics as a whole.)
  46. M

    Quantum mechanics "not quantized"

    Hi, I am currently watching this lecture series, and was wondering about something. At some point the lecturer says that QM is "not quantized", because if you express your solution to the schrodinger equationby introducing a pertubation parameter \epsilon, you will go smoothly from one...
  47. S

    Derivative of unit step function

    Homework Statement Show that δ(x-x') = d/dx Θ(x-x') Homework Equations ∫ f(x') δ(x-x') dx' = f(x) Θ(x-x') vanishes if x-x' is negative and 1 if x-x' is positive The Attempt at a Solution I saw a relation of the δ function but I don't know why is it like that. Integral of δ(x-x') from -∞ to x...
  48. S

    Self study towards quantum mechanics, string theory etc.

    Hello, before I start off, I apologize for asking a question which I am sure has been asked hundreds of times before: but I felt there is just way too much information out there which is a little confusing, so I am here with the hope of getting some personalized suggestions. I am currently a...
  49. K

    Time Asymmetry in Quantum Mechanics

    Hi all, I am reading the book "Emperor's New Mind" and have a question related to time asymmetry in state vector reduction (p.458) in quantum mechanics. Consider the following situation, as presented in the book: Suppose I have closed room with a lamp L, which emits light in some fixed...
  50. A

    Big Data in Physics: Quantum Mechanics/Particle Physics for Undergrads?

    I am an undergraduate physics major and I am taking a course on Big Data analytics. For the semester project, our professor has asked up to take up any field that interest us and do a project in that. I want to do something related to quantum mechanics or particle physics. Is that possible at my...
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