Questions tagged [quantum-mechanics]

Question 1

Given a set of non-negative real numbers $c_1, c_2, ..., c_N$, and a positive real number $D$ where $D << 1$, find an upper bound of the function: $Q(x_1, x_2, ..., x_N)$ = $\sum_{i=1}^{N}{x_i\,...

Question 2

The formula for the nth eigenstate of the QHO can be calculated from the ground state as follows: $$ |n \rangle = \frac{(\hat{a}^{\dagger})^n}{\sqrt{n!}}|0\rangle. $$ Where $\hat{a}^{\dagger}$ is $\...

Question 3

It feels to me the answer must be no because the circumstances have changed however subtly. Is there a Mathematical name for this - is it determinism, causality, chaos theory? Another example: There ...

Question 4

I am studying a recent paper (MDPI Information, 2025) that proposes a topological representation of bipartite qubit states. In the topological framework proposed, measurement outcomes are obtained by ...

Question 5

I am trying to understand the proof given in Conway's "A course in Functional Analysis" X.1.12, where it states that, given the operator $P: \mathscr{E} \to L^2([0,1])$ $\; \psi \mapsto i\...

Question 6

In the interaction picture of quantum mechanics, I want to compute an operator integral of the form $$I(t) = \int_0^t e^{iA\tau} B e^{-iA\tau}\, d\tau,$$ where $A$ and $B$ are finite-dimensional ...

Question 7

I have learnt in linear algebra that a tensor is defined via a multi-linear map from a vector space $V$ (its dual space $V^*$) onto the field, usually $\mathbb{R}$ or $\mathbb{C}$. In classical ...

Question 8

I have a to find the wave-function of the following problem. I have free spineless fermions in a 2D box trap of size $L_x\times L_y$. To such problem, the solution is known and is $$\Psi(x,y) =\sqrt{\...

Question 9

I have a question about an equation that is so simple that I feel like it should have a name and be analyzed, but I can't find a reference for it, so I am hoping someone here has seen this before. I ...

Question 10

What is the Haar measure on the Bohr compactification $b\mathbb{Z}$ of the integers? We (my collaborators and I) suspect that it is $$ \int_{b\mathbb{Z}} d\mu_H f(n) = \lim_{N\to\infty}\frac{1}{2N+1} \...

Question 11

Let's consider a Schwartz kernel as a kernel as defined by the Schwartz kernel theorem. I'm assuming one can write it in terms of an integral $$ \langle K, \phi\otimes\psi\rangle = \int K(u,v)\phi(u)\...

Question 12

This is a question that popped up while reading Greiner's Quantum Mechanics Symmetries, which I first asked on PhysSE. It was suggested that I ask the question on MathSE for better rigor. For the sake ...

Question 13

I'm currently trying to understand the action of a unitary operator on $L^2(\mathbb{R})$ (as a complex Hilbert space). For instance, let's assume we have an operator $P\colon D(P) \to L^2(\mathbb{R}), ...

Question 14

Is the space $AP(\mathbb{R})$ of Bohr's almost-periodic functions dense in $L_2(b\mathbb{R},d\mu_H)$, where $b\mathbb{R}$ is the Bohr compactification of the reals and $d\mu_H$ is the Haar measure on $...

Question 15

How to get $\langle x|p \rangle$, just by using $[\hat{x},\hat{p}]=i\hbar$, and $\langle x^{\prime}|x^{\prime\prime} \rangle=\delta(x^{\prime}-x^{\prime\prime}),\langle p^{\prime}|p^{\prime\prime} \...

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Questions tagged [quantum-mechanics]

Find the maximum of the following function $Q(x_1, x_2, ..., x_N)$ subject to some constraints.

Fractional states for the quantum harmonic oscillator

You skip a go on roulette and your number comes up. But would it necessarily have come up if you had placed the bet? [closed]

Topological Representations of Bipartite Qubit States from a new perspective

Showing $Pf = if'$ is self-adjoint on certain domain.

Efficient evaluation of $\int_0^t e^{iA\tau} B e^{-iA\tau}\, d\tau$ for large time-independent $A$

Looking for a Basis-Free Definition of a Tensor Operator in Quantum Mechanics

Series of potentials in box trap wave-function

Interpretation of an equation arising in matrix perturbation on the inner product of eigenvectors, weighted by eigengaps

What is the Haar measure on the Bohr compactification $b\mathbb{Z}$ of the integers?

Schwartz kernel mapping

Showing that the angular momentum operators and Laplace-Runge-Lenz operator together are generators of $SO(4)$

How to derive the action of the unitary operator $e^{iP}$ on $L^2(\mathbb{R})$?

Is the space $AP(\mathbb{R})$ of Bohr's almost-periodic functions dense in $L_2(b\mathbb{R})$ ($b\mathbb{R}$ is the Bohr compactification)

how to get the plane wave function, just by using commutation relation of the canonical momentum and coordinate? [closed]

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