As of May 31, 2023, we have updated our Code of Conduct.

# Questions tagged [mathematical-physics]

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

2,265 questions
Filter by
Sorted by
Tagged with
17 views

### Error in linear interpolation of $n$-dimensional curves [migrated]

Let's assume we are given an $n$-dimensional smooth curve $\gamma:[a,b] \rightarrow \mathbb{R}^n$ and $N$- sampled points $\{x_1,...,x_N\}$ of that curve. Now we use linear interpolation (or a higher ...
250 views

### Pre-requisites for V.I. Arnold's mathematical methods for classical mechanics

I am an undergraduate, studying physics. I have studied maths courses like Groups, Linear Algebra, Real analysis, Differential geometry and probability. I wish to get into mathematical physics, ...
40 views

180 views

### What "goes wrong" in a Sommerfeld expansion?

Let $f$ be the Fermi function and $H$ be a function which which vanishes as $\epsilon \to -\infty$ and which diverges at $\infty$ no worse than some power of $\epsilon$. In the Sommerfeld expansion of ...
75 views

### Is it physically relevant to restrict the solution of a nonlinear PDE to positive frequencies in the Fourier transfrom?

I would like to mention that I am a mathematician and not a physicist, so I apologize in advance if my question seems obvious. Considering any linear PDE, it is common to understand the behavior of ...
30 views

### Discrete symmetries of Hamiltonian and Change of Representation

In quantum mechanics, one could write Hamiltonians for a given quantum system both in coordinate and momentum spaces as mentioned for example in Sakurai book. Does the discrete symmetries such as ...
43 views

### Projective representations and central extensions- classification in terms of $H^2(G,\mathbb{C}^{\times})$

In quantum mechanics, unitary projective representations play a crucial role. To be more general, I want to pose the question in sense of projective representations, then everything would follow as a ...
1 vote
48 views

### Spectrum and Schrödinger equation [duplicate]

The time-evolution in quantum mechanics is given by Schrödinger's equation. For time-independent Hamiltonians, one searches for solutions of the problem $\hat{H}\psi = E\psi$. The physicist point of ...
41 views

### What's the ladder operator of Duffing Oscillator?

I know the ladder operator for harmonic oscillator can be obtained by factorization method, can the same method be applied to oscillators with potential $V(x)=x^{4}$ (the Duffing case) or higher ...
80 views

### 2D CFT from sigma models

$X$ is a closed manifold with a positive-definite metric $g$. $M_2$ is a 2D oriented closed manifold with a positive-definite metric $G$ and a compatible volume form $\omega$. We can then consider the ...
82 views

### Generalization of Bargmann's theorem

Bargmann's theorem is usually stated for a simply connected Lie group with vanishing second Lie algebra cohomology $H^2(\mathfrak{g},\mathbb{R})$. I found a generalization of this result in a thesis ...
1 vote
109 views

### Projective representations and cental extensions based on Schottenloher's book

In Schottentloher's book, a theorem is stated: Later on, a remark is made: My confusion comes: Is E always of the form made in the remark, namely are the following to sets equal(up to set theoretic ...
74 views

165 views

### Is linear momentum quantized in quantum harmonic oscillator

I'm self-studying QM and have a basic question on quantum harmonic oscillator. The Hamilton is certainly quantized under this model, that is $E_n=(n+1/2)\hbar \omega$, for $n=0,1,2,...$. But is linear ...
1 vote
71 views

### Experiment design: can one actually measure the speed of non-local light in curved spacetime

The equivalence principle tells us that in some local neighborhood, every free-falling observer in a general relativistic spacetime will measure the speed of light to be $c$; this literally means at a ...
242 views

### Adjoint of the Quantum Momentum Operator

I'm studying quantum mechanics and I have a question about the momentum operator. We have that the momentum operator is given by \begin{equation*} p = -i\hbar\nabla \end{equation*} and so its adjoint ...
180 views

### HaMiDeW coefficients - recursive calculation of the coincidence limits

In his book Aspects of Quantum Field Theory in Curved Spacetime Stephen Fulling calculates the coincidence limit $[a_1]$ and gives an idea of how $[a_n]$ with $2 ≤ n$ can be found recursively. Since ...
211 views

### The spectrum of the Hamiltonian in quantum mechanics

Consider the Hilbert space $\mathscr{H} = L^{2}(\mathbb{R}^{d})$ and a Hamiltonian: $$H = -\frac{\hbar^{2}}{2m}\Delta + V(x)$$ for some potential function $V$. States of well-defined energy $E$ are ...
1 vote