Dec 6, 2018 · 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 …

Jan 19, 2011 · What exactly is an eigenfunction, and what are some of the applications of an eigenfunction?

Sep 3, 2007 · Notice that you are not required to find an eigenfunction- you are already given it. You only need to show that this function is an eigenfunction by applying the operator to it and showing …

Is there a difference between "eigenfunction" and "eigenstate"? They seem to be used interchangeably in texts, which is confusing. My guess is that an "eigenfunction" has an explicit representation/

Feb 20, 2021 · The discussion demonstrates that the spherical harmonic Y 1, 1 (θ, ϕ) is an eigenfunction of the operator L ^ 2, yielding an eigenvalue of 2 ℏ 2 after applying the operator.

Apr 10, 2020 · Since these two operators commute, we can choose the eigenfunctions that are the eigenfunctions of both these operators. The opposite however is not necessarily true: if the …

Nov 5, 2023 · The argument usually goes about splitting the sine into a sum of complex exponentials, and thus getting $\pm \hbar k$ as eigenvalues, and, since a superpositions of eigenvalues isn't …

It would be very useful if you specify which book you are using. Sounds like it is a choice of eigenstate for both Hamiltonian and Momentum since $ [H, p] = 0$ for a free particle.

May 23, 2018 · The physical (ist) approach (I will ignore factors of $2\pi$, so forgive me for that :) ) is looking to solve the eigenfunction equation of the momentum operator (obviously real values, since …

Dec 29, 2007 · Eigenfunction, Eigenvalue, Wave Function and collapse birulami Dec 29, 2007 Collapse Eigenfunction Eigenvalue Function Wave Wave function