What is eigenvalue and eigenfunction in quantum mechanics?
2018年12月6日 · Each eigenfunction (of the Hamiltonian) is the state of the system when its energy is equal to the associated eigenvalue. This can be compared to the study of a vibrating string in classical mechanics---a useful thing to know is the frequency of the fundamental mode and all the other modes, and the shape of the string for each case.
Is u(x) = exp(-x²/2) an Eigenfunction of \hat{A} = d²/dx² - x²?
2007年9月3日 · Eigenfunction Operator. In summary, to prove that u (x)=exp (-x^ {2}/2) is the eigenfunction of \hat {A} = \frac {d^ {2}} {dx^ {2}}-x^2, you can apply the operator to the function and show that it is a multiple of the function. If you do not know the eigenfunction in the beginning, you can find it by solving the differential equation Au = au.
quantum mechanics - Is an eigenfunction a probability density ...
2022年3月29日 · There is no such thing as “a probability density to give a specific eigenvalue”; in fact this is in a sense self contradictory as a probability density implies there is a distribution of outcomes rather than a specific one. When the system is described by the eigenfunction of an operator, there is 100% probability that the measurement of ...
quantum mechanics - When Eigenfunctions/Wavefunctions are …
All bound states can typically be chosen to have real-valued wavefunctions. The reason for this is that their wavefunction obeys a real differential equation, − ℏ2 2m∇2ψ(r) + V(r)ψ(r) = Eψ(r) − ℏ 2 2 m ∇ 2 ψ (r) + V (r) ψ (r) = E ψ (r) and therefore for any solution you can construct a second solution by taking the complex ...
quantum mechanics - Can we solve the general eigenfunction of …
2020年7月24日 · The problem lies in your understanding of the operator algebra and Hilbert spaces not so much on your calculus I think.
Common eigenfunctions of commuting operators: case of …
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What is exactly eigenfunction in quantum mechanics? [closed]
2017年9月20日 · The eigenvalue problem of a real operator A^ A ^ is technical but basic in quantum theory. It consists on finding every pair of real number x x and ket |α | α satisfying the eigenvalue equation: Aˆ|α = |α x. A ^ | α = | α x. |α | α is the eigenket and x x is the eigenvalue. If you have a generalized orthonormal basis x| x | you can ...
Energy Eigenfunction Completeness - Physics Stack Exchange
2. You have to be a bit more careful. When you say that "momentum eigenfunctions are complete with respect to any potential" you're saying that any function can be decomposed as f(x) = ∫dp 2π eipxˆf(p), ˆf(p) = ∫dxe − ipxf(x). But this is formal nonsense: for a general function f(x), the integral defining ˆf(p) doesn't exist (it ...
Is Ψ2Px an Eigenfunction of L2 or Lz in Quantum Mechanics?
2016年4月7日 · Eigenfunction L2 Operator. In summary, the conversation discusses the use of operators and eigenfunctions in quantum mechanics, specifically in relation to the real wave function Ψ2Px and its potential as an eigenfunction of L2 or Lz. The notation and terminology used are also explained, including the use of quantum numbers and the spdf notation.
Eigenfunctions v.s. eigenstates - Physics Stack Exchange
They seem to be used interchangeably in texts, which is confusing. My guess is that an "eigenfunction" has an explicit representation/argument, e.g. in terms of position, x x, whereas an "eigenstate" is abstract. Thanks in advance for any clarification! :) But then again, some texts violate this rule, so I'm prolly wrong...