# Tagged Questions

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, ...

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### Does the Hermitian operator $H=-\frac{d^2}{dx^2}$ have imaginary eigenvalues?

In quantum mechanics, Hermitian operators play a very important role because they possess real eigenvalues. Considering $-\frac{d^2}{dx^2}$, it is a Hermitian operator (Actually it's the simplest ...
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### Minimizing a damping constant in order to minimize the amplitude of oscillations

How can I determine the damping coefficient that minimizes the amplitude of vibrations? This is an extension of Coupled ODEs that model a quad rotor \begin{align} ...
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### Physical observables and hermiticity

Is it necessary for an operator to be Hermitian in order to be a physical observable or is it just sufficient that the operator obeys the eigenvalue equation? If I were to check whether an operator is ...
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Consider a system of particles with wave function $\psi$(x) (x can be understood to stand for all degrees of freedom of the system; so, if we have a system of two particles then x should represent {$... 1answer 223 views ### Are Negative Eigen Values of a Hessian Matrix physically acceptable? Suppose I have a Hessian Matrix of a System with 3N degrees of freedom, What are the physical significance of eigen values of the Hessian, Are negative Eigen Values physically acceptable? 4answers 173 views ### Help understanding proof in simultaneous diagonalization The proof is from Principles of Quantum Mechanics by Shankar. The theorem is: If$\Omega$and$\Lambda$are two commuting Hermitian operators, there exists (at least) a basis of common eigenvectors ... 2answers 138 views ### Momentum Operator in Quantum Mechanics 1) What is the difference between these two momentum operators:$\frac{\hbar}{i}\frac{\partial}{\partial x}$and$-i\hbar\frac{\partial}{\partial x}$? How are these two operators the same? My ... 2answers 613 views ### Eigenenergies and eigenkets given the Hamiltonian For a two level system the Hamiltonian is: $$H=a(|1\rangle \langle1|-|2\rangle\langle2|+|1\rangle\langle2|+|2\rangle\langle1|)$$ where$a$is a number with the dimension of an energy. I need to ... 1answer 148 views ### Meaning of Eigenvalues/Eigenvectors of a linear system of equations I have a 41x41 system of linear equations (inhomogen) which I derived with Eureqa by describing the timecourse of fMRI haemodynamic data from a brain area as a function of the timecourses of 40 other ... 2answers 283 views ### Eigenvalue problem for differential equations in QM I have a very simple question with regard to numerical methods in physics. I want to solve the eigenvalue problem for a particle moving in an arbitrary potential. Let's take 1D to be concrete. I.e. I ... 1answer 175 views ### Eigenvalues of Infinite Dimensional Matrix [duplicate] If I take a infinite-dimensional square matrix, what can I say about its eigenvalue spectrum? Will they have a discrete infinity of eigenvalues or continuous infinity of them? 1answer 439 views ### Imaginary Eigenvalue Of A Hermitian Operator The eigenfunctions of a Hermitian operator are real. But consider a function$\psi(x)=e^{-\kappa x}$,$x\in\mathbb{R}$, where$\kappa$is a real constant. Then, $$\hat p \psi(x)=-i\hbar \frac{d}{dx}e^{... 1answer 361 views ### Diagonalize a dot product with Pauli matrices How can I diagonalize the following operator?$$\lambda \hat{\vec{\sigma}}\cdot\vec{r}$$where$\lambda$is a real constant,$\hat{\vec{\sigma}}=(\hat{\sigma_{x}},\hat{\sigma_{y}},\hat{\sigma_{z}}) $... 1answer 574 views ### Proof of the time-independent Schrödinger equation I have a question regarding the proof of the time-independent Schrödinger equation. So if we have a time-Independent Hamiltonian, we can solve the Schrödinger equation by adopting separation of ... 1answer 581 views ### Spin eigenvalues and eigenvectors problem. Is this the correct way to solve it? An electron is described by the Hamiltonian$ H=\frac{e}{mc}\bar{S}\cdot\bar{B} $where$\bar{S} =(S_x,S_y,S_z)$is the spin operator and$\bar{B}$the magnetic field. For$t>0\bar{B}=B_0\hat{...
Context: The question refers to computational physics of non linear systems with Mathematica. Excercise: Given the system $\{f_1: \dot{x} = a x + y + x^3, f_2: \dot{y} = x - y \}$: Find the ...
I'm studying perturbation theory in the context of quantum mechanics. My lecture notes say that in order to calculate the first-order correction of eigenfunction $\psi_n$, that is $\psi_n^{(1)}$, I ...