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. Ryaners

    Electron in 1-D box: photon absorbed?

    I don't know where I'm going wrong with this problem - I was so sure I had it right but the online grader tells me otherwise :oldfrown: Homework Statement An electron in a one-dimensional box has ground-state energy 2.60 eV. What is the wavelength of the photon absorbed when the electron...
  2. KarminValso1724

    B Does quantum mechanics explain why subatomic particles behave the way they do?

    For example, general relativity relates the behavior of gravity the the deformation of spadetime. But does quantum mechanics explain why particles behave the way they do? Or does it only explain how processes such as entanglement work not why they occur.
  3. DrPapper

    I Expression for Uncertainty of Arbitrary Operator

    Hello all, as far as I can see this question is not posted already, my apologies if it is and please provide a link. But I'm watching this video on youtube: And at 22:38 there's an expression given for the uncertainty of an arbitrary operator Q, however I'm concerned the expression is incorrect...
  4. E

    I Energy of a number of particles

    Hello! It is sometimes useful to find the average energy of a certain number N of particles contained in a box of volume V. In order to find this quantity, the total energy is required and then divided by N. The result is E_{average} = \displaystyle \frac{1}{N} \sum_{n = 1}^{N} \left| a_n...
  5. thegirl

    I Why is there only odd eigenfunctions for a 1/2 harmonic oscillator

    Hi, why there is only odd eigenfunctions for a 1/2 harmonic oscillator where V(x) does not equal infinity in the +ve x direction but for x<0 V(x) = infinity. I understand that the "ground state" wave function would be 0 as when x is 0 V(x) is infinity and therefore the wavefunction is 0, and...
  6. michaelmolli

    Particle in One-Dimensional Box Problem [Quantum Mechanics]

    Homework Statement a) Determine the ratio (Em/En) between two energy states of a particle in a one dimensional box of length l. b) Show that this is consistent with the non-relativistic low-energy limit. The attempt at a solution I have figured out a) using the de broglie wave-particle duality...
  7. F

    Quantum Mechanics: Delta Potential Sudden Change

    Homework Statement I have a particle which is initially in a bound state for a given voltage in the form of a delta function at the origin, V = -αδ(x) initial state is ψα = (√αm)/h2*exp(-m*α*|x|/(h2) At t=0, voltage is changed to V = -βδ(x) both α and β are greater than zero. Right now I'm...
  8. Schwarzschild90

    Transfer matrix for a finite length? (Quantum mechanics)

    Homework Statement I'm struggling to find a solution to exercise (*b). I have uploaded a pdf of the assignment. Please advise me at your convenience. Homework Equations x(x_l^+) = T(x_l^+, x_l^-)x(x_l^-) The Attempt at a Solution x(a^-) = \frac{\psi(a^-)}{\psi(a^-)} , T(a^+, a^-) \left(...
  9. J

    I How to prove Schrodinger's equation in momentum space?

    Specifically, i do not know hot to express the potential in momentum space. If someone would provide me with a link of source that has the proof in it, it would be appreciated.
  10. A. Neumaier

    A Effective Dynamics of Open Quantum Systems: Stochastic vs Unitary Models

    Not quite. But it necessarily has to be described by a different quantum model than unitary dynamics if it is an open system and the rest of the universe is not explicitly modeled. For convenience, physicists often want to describe a small quantum system in terms of only its Hilbert space, when...
  11. Danny Boy

    I Why is reflection coefficient defined this way

    In Griffith's "Introduction to Quantum Mechanics, second edition" he states: For the delta-function potential, when considering the scattered states (with E > 0), we have the general solutions for the time-independent Schrodinger equation: $$\psi(x) = Ae^{ikx} + Be^{-ikx}~~~~\text{for }x<0$$ and...
  12. E

    Free Particle moving in one dimension problem

    Homework Statement 5) A free particle moving in one dimension is in the state Ψ(x) = ∫ isin(ak)e(−(ak)2/2)e(ikx) dk a) What values of momentum will not be found? b) If the momentum of the particle in this state is measured, in which momentum state is the particle most likely to be found? c)...
  13. A. Neumaier

    I Postulates for the formal core of quantum mechanics

    I'll answer this in this thread, later today.
  14. Imran Makhdoom

    B Quantum mechanics and reality of matter

    Hi Do Quantum Mechanics negates the reality of matter and proves un-reality of matter ?
  15. F

    Why do we need Quantum Mechanics so much?

    Almost phenomena at macro level are classical phenomena,why physics needs QM very much?Is it rational need or practical need?
  16. M

    Quantum non-locality and vacuum polarization

    Quantum particles are not localized before they are observed, as shown with the Young double slit experiments and those with entangled particles. On the other side, vacuum is filled with virtual particles. Are the non-localized particles responsible for the virtual particles? or only for a part...
  17. weezy

    How does the formula C-6 come about in the following image?

  18. aleazk

    Tools to enrich our quantum mechanics interpretations discourse - Comments

    aleazk submitted a new PF Insights post Tools to Enrich our Quantum Mechanics Interpretations Discourse Continue reading the Original PF Insights Post.
  19. C

    B Quantum Mechanics vs. Pilot-Wave thought experiment

    Hello. I want to share a thought experiment that could tell Quantum Mechanics apart from Pilot-Wave interpretation. It goes like this: Quantum Mechanics vs. Pilot-Wave: Quantum Mechanics: Waves collapse to particles. Waves disappear when particles are detected. Pilot-Wave: Waves are real but...
  20. G

    Harmonic oscillator positive position expectation value?

    So this is something that troubled me a bit- in Shankar's PQM, there's an exercise that asks you to find the position expectation value for the harmonic oscillator in a state \psi such that \psi=\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle) Where |n\rangle is the n^{th} energy eigenstate of...
  21. T

    Why is the electromagnetic field not a 'charge field'

    This question is a continuation/topic-extrapolation of: https://www.physicsforums.com/threads/flux-in-magnetic-core-according-to-special-relativity.856482/#post-5374651 My question is 'how is the electromagnetic field different from some sort of mere electric-charge field?' The issue I have...
  22. omidaut

    Advanced quantum mechanics book with solutions

    Hi there! Can you please introduce me some books on advanced quantum mechanics which has solutions for its exercises. Of course, I know Shankar and Sakuraii, but, I mean something more advanced which covers these topics: (Scattering, Dirac Fields, Group Representations, Relativistic Quantum...
  23. DaTario

    A Amplitudes of probability in Mathematics before QM

    Hi All, Was there any use of the concept of amplitudes of probability before their use in quantum mechanics? In connection to this question, who invented or was the first to use this resource? Best wishes, DaTario
  24. C

    How do I evaluate <x> with the k-space representation?

    Homework Statement Given the following k-space representation of the wave function: Ψ(k,t) = Ψ(k)e-iħk2t/2m use the wave number representation to show the following: <x>t=<x>0 + <p>0t/m <p>t=<p>0 Homework Equations <x>=∫Ψ*(x,t)xΨ(x,t)dx <p>=∫Ψ*(x,t)(-iħ ∂/∂x)Ψ(x,t)dx The Attempt at a...
  25. smodak

    Quantum Spin First Approach to Quantum Mechanics Textbook

    So far I have seen Sakurai, Townsend, Cohen Tannoudji, Feynman, and McIntyre. Are there any other books that take this approach? Just curious.
  26. W

    Berry's Curvature Equation cross product calculation

    Hi, The following textbook Heisenberg's Quantum Mechanics shows an example of calculating Berry's curvature (top page on pg 518). It led to a following equation Vm= (- 1/B2 ) * i *∑ ( <m,B|S|n,B> ∧ <n,B|S|m,B> ) / A2 ...[1] the textbook claims that we add the term m = n since <m|S|m> ∧ <m|S|m>...
  27. M

    Quantum Ballentine's book: 1st or 2nd edition?

    I'm planning to get a copy of Quantum Mechanics - Modern Development by L. E. Ballentine. However I am uncertain between the first and second editions. The first edition is cheaper. I will be using it for my PhD research with the topic of atomic physics. Will the second edition give me...
  28. L

    Finding the State of a Quantum System with Given Hamiltonian and Observable

    Homework Statement We are given the Hamiltonian H and an observable A ##H=\begin{pmatrix} 2 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0 \end{pmatrix}\hbar\omega A= \begin{pmatrix} 1 & 0 & 0\\0 & 1 & 0\\0 & 0 & -1 \end{pmatrix}a ## We are also told that at ##t=0## we have that a measurement of A gives us...
  29. 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 ...
  30. 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?
  31. 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...
  32. 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...
  33. 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...
  34. 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...
  35. 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...
  36. 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.
  37. 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...
  38. 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.
  39. 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...
  40. 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...
  41. 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...
  42. 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!
  43. 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...
  44. 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
  45. 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?
  46. 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.
  47. 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...
  48. 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...
  49. 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?
  50. 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...
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