What is Quantum-mechanics: Definition and 17 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. P

    I 100 boxes of Length L, an application of the famous Particle in A Box

    Suppose I have 100 identical boxes of length L and the coordinates are x=0 at one end of the box and x=L at the other end, for each of them. Each has a particle of mass m. V=0 in [0,L], while it's equal to infinity in the rest of the regions. If I make a measurement on position of the particle...
  2. S

    I The Multiverse and 'No boundary' conditions approach in cosmology

    Summary: Questions about the Multiverse hypothesis and the 'No boundary' conditions approach in cosmology I have some questions about James Hartle and Stephen Hawking's 'No-boundary' proposal: - In their approach multiple histories would exist. These histories could yield universes with...
  3. dude2

    A Aharonov - Bohm effect exercise

    Does anyone know the answers to this, or can hopefully guide me to a text that will help me solve this aharonov-bohm problem? Here is the given: Particles (of mass m, and charge q), are driven through two slits that have distance d between them, in a screen that is far away (L>>d) from the...
  4. D

    How to find the expectation value of cos x

    Homework Statement If x is a continuous variable which is uniformly distributed over the real line from x=0 to x -> infinity according to the distribution f (x) =exp(-4x) then the expectation value of cos 4x is? Answer is 1/2 Follow· 01 Request Homework Equations the expectation value of any...
  5. CharlieCW

    2D isotropic quantum harmonic oscillator: polar coordinates

    Homework Statement Find the eigenfunctions and eigenvalues of the isotropic bidimensional harmonic oscillator in polar coordinates. Homework Equations $$H=-\frac{\hbar}{2m}(\frac{\partial^2}{\partial r^2}+\frac{1}{r}\frac{\partial}{\partial r}+\frac{1}{r^2}\frac{\partial^2}{\partial...
  6. CharlieCW

    Eigenvalues dependent on choice of $\vec{A}$?

    Homework Statement A particle with spin s=1/2 moves under the influence of a magnetic field given by: $$\vec{A}=B(-y,0,0)$$ Find the eigenvalues of the corresponding Pauli hamiltonian. Repeat the same process for: $$\vec{A}=\frac{B}{2}(-y,x,0)$$ Explain your result by relating the...
  7. CharlieCW

    Coherent states for Klein-Gordon field

    Homework Statement Show that the coherent state ##|c\rangle=exp(\int \frac{d^3p}{(2\pi)^3}c(\vec{p})a^{\dagger}_{\vec{p}})|0\rangle## is an eigenstate of the anhiquilation operator ##a_{\vec{p}}##. Express it in terms of the states of type ##|\vec{p}_1...\vec{p}_N\rangle## Homework Equations...
  8. CharlieCW

    Degenerate parametric amplifier: quadratures

    Homework Statement The degenerate parametric amplifier is described by the Hamiltonian: $$H=\hbar \omega a^\dagger a-i\hbar \chi /2 (e^{(2i\omega t)}a^2-e^{(-2i\omega t)}(a^\dagger)^2)$$ Where ##a## and ##a^\dagger## as just the operators of creation and anhiquilation and ##\chi## is just a...
  9. CharlieCW

    Finding Eigenvalues of an Operator with Infinite Basis

    I just began graduate school and was struggling a bit with some basic notions, so if you could give me some suggestions or point me in the right direction, I would really appreciate it. 1. Homework Statement Given an infinite base of orthonormal states in the Hilbert space...
  10. CharlieCW

    Coherent states in quantum mechanics (Schrödinger Cat)

    Hello. I've been struggling for a day with the following problem on Quantum coherent states, so I was wondering if you could tell me if I'm going in the right direction (I've read the books of Sakurai and Weinberg but can't seem to find an answer) 1. Homework Statement *Suppose a Schrödinger...
  11. Z

    I Why the velocity operator commutes with position (Dirac equation)

    ##\hat{v}_i=c\hat{\alpha}_i## commute with ##\hat{x}_i##, ##E^2={p_1}^2c^2+{p_2}^2c^2+{p_3}^2c^2+m^2c^4## But in classical picture,the poisson braket...
  12. E

    I Delayed choice experiment clarification (specific setup)

    I know that clarifications about delayed choice experiment was asked million times, and I understand the idea, but I was not able to find the discussion of this particular situation anywhere, though I tried hard. This setup is described in Brian Greene's Fabric of the Cosmos book (note my...
  13. Q

    I Modelling Decoherence as a Transition Out of Subspace

    Modelling the onset of decoherence in a subspace as a transition from this subspace http://www.ba.infn.it/~pascazio/publications/sudarshan_seven_quests.pdf (Section 10 is relevant) I am currently reading papers discussing the Zeno Effect. The linked paper discusses modelling a transition out of...
  14. D

    Instantaneous eigenstates in the Heisenberg picture

    I'm a bit confused as to what is meant by instantaneous eigenstates in the Heisenberg picture. Does it simply mean that if vectors in the corresponding Hilbert space are eigenstates of some operator, then they won't necessarily be so for all times ##t##, the eigenstates of the operator will...
  15. D

    Conceptual questions on unitarity and time evolution

    From a physical perspective, is the reason why one requires that the norm of a state vector (of an isolated quantum system) is conserved under time evolution to do with the fact that the state vector contains all information about the state of the system at each given time (i.e. the...
  16. ambroochi

    Momentum of 1d harmonic oscillator

    The ground state wave-function of a 1-D harmonic oscillator is $$ \psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}). $$ a) find Average potential energy ? $$ \overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2} $$ b) find Average kinetic energy ? $$ \overline{T} =...
  17. N

    Exploring the Empty Space of Atoms: The Zero-Dimensional Particle Theory

    If all fundamental particles are zero dimensional, are atoms empty space? And they are zero dimensional, does that mean that we don't exist?