# Questions tagged [eigenvalue]

A linear operator (including a matrix) acting on a non-zero *eigenvector* preserves its direction but, in general, scales its magnitude by a scalar quantity *λ* called the *eigenvalue* or characteristic value associated with that eigenvector. Even though it is normally used for linear operators, it may also extend to nonlinear operations, such as Schroeder functional composition, which evoke linear operations.

488 questions
Filter by
Sorted by
Tagged with
41 views

### Measuring a state in a basis other than eigenbasis

Suppose I have a state expressed in its eigenbasis as follows. $\rho = \sum_i\lambda_i\vert i\rangle\langle i\vert$. It is now measured in some other basis $\{\vert x\rangle\}$ that is distinct from ...
72 views

81 views

### Collapse of wavefunction to its eigenfunction upon measurement

In quantum mechanics, it is postulated that to every observable, we have an associated operator. It is further postulated that when we do a measurement on a system, the measured value is one of the ...
72 views

### (How) can you tell that a given operator's eigenspectrum will feature degeneracy?

I am speaking about operators representing physical observables and am not interested in purely mathematical objects (if that's relevant to answering the question). I know that a degenerate ...
38 views

### Translation operator eigenvalues can be real and arbitrary?

Consider the translation in space operator in $1D$: $$D(a)=e^{-ia\hat{p}/\hbar}$$ It is unitary - $D(-a)=D^{\dagger}(a)=D^{-1}(a)$ - which implies that $D(a)$ has eigenvalues on the unit circle like ...
29 views

### Numerical way of finding energy spectrum of $N$-body Schrodinger equation

For a single particle trapped in a potential, one can discretize the Time Independent Schrodinger Equation and hence find the eigenvalues of the corresponding Hamiltonian by diagonalising numerically. ...
32 views

### How to choose boundary conditions for numerical solution of Schrodinger's equation whose solutions are expected to die out “at infinity”?

I am using the "Shooting method" for solving the TISE with a "reasonably arbitrary" potential in 1D,with boundary conditions such that the eigenfunctions $\psi_n\to0$ as $x\to\infty$(And another ...
53 views

### Floquet bandstructure calculation

In this paper "Photonic Floquet Topological Insulators" the authors calculate the bandstructure of a time-periodic Hamiltonian. They create a time-dependent tight-binding Hamiltonian via the Peierl's ...
36 views

### Finding the eigenvalues of a matrix with particular symmetry [migrated]

I have a matrix for which I want to get some analytical equations of the eigenvalues. The matrix is given as \begin{align} \mathbf A &= \begin{pmatrix} \epsilon_a & 0 & 0\\ 0 & \...
35 views

339 views

### What is a physical example of an observable with degenerate eigenvalues? [closed]

If eigenvalues of an observable have the physical meaning of a possible result after a measurement, what's the interpretation of degenerate eigenvalues, and what is an example of such an observable?
57 views

31 views

92 views

### How do you find the Triangle Inequality from an Inertia Matrix?

If you have an inertia matrix of the form $$\begin{pmatrix} I_{xx} & I_{xy} & I_{xz} \\ I_{yx} & I_{yy} & I_{yz} \\ I_{zx} & I_{zy} & I_{zz} \end{pmatrix}=I$$ If the matrix ...
65 views

### Determining What Eigenfunction Occurs With Wavefunction Collapse

Suppose an operator $O$ has eigenfunction normalized $f$ corresponding to eigenvalue $n.$ Of course, any function $cf$, with $c$ on the unit circle, is also a normalized eigenfunction. Thus, if a ...
35 views

73 views

### Are eigenfunctions always normalizable?

If $y$ is an eigenfunction which corresponds to the eigenvalue $a$ of the operator $A$: $$A\langle y|=a\langle y|$$ Can we assume that $$\int y^*y=1$$ ?
77 views

### Is the mass an eigenvalue of Dirac equation?

Writing the Dirac equation as: $$(i \hbar\gamma^{\mu}\frac{\partial}{\partial x^{\mu}})\psi = m \psi$$ it seems that $m$ is an eigenvalue of the operator of the left side, and we need to find the ...
277 views

### Proof that coherent states are eigenstates of annihilation operator [closed]

My goal is to prove that, for $|\lambda\rangle=N\exp(\lambda\hat{a}^\dagger)|0\rangle$ is an eigenvector of the operator $\hat a$. I took 2 approaches, but both make sense to me and I get different ...
84 views

### Why is $|\alpha\rangle$ not eigenstate of $a^{\dagger}$ for $\alpha^*$

I know that even if we have: $$a |\alpha \rangle = \alpha |\alpha\rangle$$ We don't have: $$a^{\dagger} |\alpha \rangle = \alpha^* |\alpha\rangle$$ Actually as explained in the second answer here ...
70 views

183 views

The textbook says the eigenvalue of the Pauli y matrix is 1 and -1, the corresponding eigenvectors are, $$\sqrt{\frac{1}{2}} \begin{bmatrix} 1\\ i \end{bmatrix} , \sqrt{\frac{1}{2}} \begin{bmatrix} 1\... 1answer 52 views ### What is an interaction (Quantum Mechanics) and is the wavefunction collapse an objective phenomenon? First of all, I'm an undergrad. student of engineering physics, so I must explicit my lack of formal knowledge on the subject and total confusion with its implications. I also understand it may be ... 1answer 57 views ### Hydrogen wave function and angular momentum operators [closed] I'm working my way through an old exam assignment for my Introduction to Quantum mechanics and a few (parts of) questions have me a little confused. The assignment is about the hydrogen atom and its ... 0answers 47 views ### Relation between irreducible representations and eigenstates When in quantum mechanics the Hamiltonian possesses some symmetry, then knowing the irreducible representations of the group to which the symmetry belongs gives information about the eigenstates. As ... 0answers 84 views ### Eigenstates and eigenvalues of the operator xp+ px [duplicate] It is a hermitian operator, right? So, what are its eigenstates and eigenvalues? It is known that it is the infinitesimal generator of the dilation group in 1d. But apparently, a nontrivial dilation ... 2answers 93 views ### Momentum operator and eigenvalue Can we take the eigenvalue we obtained after momentum operator (of quantum mechanics) operates on the state vector of a system as the momentum of the system? 1answer 39 views ### Completeness relation, commuting operators I have a question about some formulars our professor wrote on the black board. Let \hat{Q}_{1},...,\hat{Q}_{N} be operators, which are a CSCO. We know now that there exists a set of eigenvectors \{... 1answer 76 views ### Eigenvalues of the momentum operator in position basis We know that the definition of the momentum operator \hat{P_x} in an state space \mathcal{E} is:$$\hat{P_x}|\psi\rangle=P_x|\psi\rangle$$where P_x \in \mathbb{R}. However we also know that ... 1answer 39 views ### Does the energy eigenvalue have a position dependence? I would like to transform the time independent Schrodinger equation from position to momentum space, but I am stuck on one point: Does the energy eigenvalue act as a unchanged diagonal matrix or does ... 0answers 27 views ### doubt about Bogoliubov for diagonalize matrix I have the following equations:$$\begin{pmatrix} \dfrac{d}{dt}C \\ \dfrac{d}{dt}C^{*} \end{pmatrix}= - \dfrac{1}{i} \begin{pmatrix} A& B \\ -B^{*} & -A^{*} \end{pmatrix} \begin{...
Is there any sensible meaning of the term eigenfunctionals? The object I want to describe is a solution to the following equation $${\mathscr D}_x F[g] = f(x) F[g]$$ where ${\mathscr D}_x$ is an ...
I was trying to reproduce the results of an exercise where they calculate the normal modes of oscillation. \begin{pmatrix} \dfrac{d}{dt}C \\ \dfrac{d}{dt}C^{*} \end{pmatrix}= - \dfrac{1}{i} \...