# Questions tagged [mathematics]

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 The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

1,184 questions
Filter by
Sorted by
Tagged with
10 views

### Coupled Resonators with sinusoidal coupling [closed]

I have two coupled resonators with complex resonance frequencies of $\beta_1$ and $\beta_2$. The coupling between them is varying sinusoidal with time. The time-evolution of their resonant mode field (...
46 views

### Characteristic classes and index theorems for physicists

Since characteristic classes and index theorems are occasionally used in the QFT (for example, when discussing instantons or quantum anomalies), I want to learn more about them. Is there any good ...
51 views

### The Weird Interpretation for Contravariant and Covariant Vector

I have seen the answer for related topics, and it makes sense to me for the trivial contranvariant expression for a vector, $$\pmb{v} = v^i\hat{e}_i\tag{1}$$ and it is said that if the base $\hat{e}_i$...
33 views

### Finding numerical solution of differential equation [closed]

I investigated my system and encountered differential equation such as $y''(x) = e^{y(x)}-e^{-2y(x)}-e^{y(x)-y(x+d)}$, where $d$ is a constant. I can write python script rest of the thing, but I ...
21 views

### Can this problem be sloved by calculation in coordinate system [closed]

Point M is the shared point of line AB ande the circle,and you need to calculate the acceleration of piont M at the moment that is shown on the picture
1 vote
43 views

### Why there is only one modulus for a Klein bottle?

In Polchinski Page 207, there is a claim that only one modulus for a Klein bottle, I tried to understand this claim, Here's what I have tried: As I understand, modulus means the geometries that are ...
54 views

### How do we know the geometry of our physical world is made from real numbers and not rational numbers? [duplicate]

If I draw a line on a paper from point a to point b, how do we know that each point on the line exists in the real space, and not the rational space? How do we know if I randomly draw a dot, it won't ...
105 views

### What does it mean to transform a tensor?

My electrodynamics lecture only defines a tensor (in $R^3$) of rank $n$ as a "set of quantities $T_{i_1i_2...i_n}$, $i_1, ... i_n = 1,2,3$ that transforms under rotation as follows: \begin{...
84 views

### Scalar Product Calculation and Identical Particles in Quantum Mechanics

In the book "Nolting, Theoretical Physics Part 5/2" (German), on Page 264, Formula 8.80, the author introduces second quantization in the case of identical particles. One considers the ...
20 views

### How to obtain approximation solution for this differential equations? [migrated]

I am looking for approximation solution for this differential equations \begin{align*} & \ddot{x}=-2\,\Omega\,\cos \left( \phi \right) {\dot z}+2\,\Omega\,\sin \left( \phi \right) {\dot y}\\ &...
1 vote
10 views

### Is the character table of $S_3$ unique? [migrated]

I'm trying to construct the character table of $S_3$ group. $n_c$ class $1$ $\bar{1}$ $2$ 1 $I$ 1 1 2 3 $(12),(23),(13)$ 1 a b 2 $(123),(132)$ 1 c d As a brute force method, I imposed every ...
58 views

### Reference for mathematics of quantum mechanics with infinite degrees of freedom?

I am looking for a book, or lecture notes or even courses available on YouTube where there is a good and detailed discussion on the mathematical aspects of Quantum Mechanics with infinite degrees of ...
122 views

### Do matrices with this property appear in physics?

First I should mention that my background is in Mathematics, but I am looking for a motivating example in physics. I apologize in advance if my question does not meet the standards of this site. ...
98 views

### Eigenvalues of an time-ordered exponential operator

Let's consider a simple 1-qubit time-dependent Hamiltonian: $$H(t) = \delta(t) \sigma_x + \sigma_z \ ,$$ where $\delta(t)$ is some time-continuous (real-valued) function. Evolving $H(t)$ continuously ...
1 vote
61 views

### Lagrangian total time derivative - continues second-order differential

In the lagrangian, adding total time derivative doesn't change equation of motion. $$L' = L + \frac{d}{dt}f(q,t).$$ After playing with it, I realize that this is only true if the $f(q,t)$ function has ...
1 vote
26 views

### After equation (1.6) the author said that "The sequence of integration and limiting process in Eq. (1.6) must not be interchanged" but he interchanged [migrated]

In the attached screenshot, after equation (1.6) the author stated clearly that the sequence of integration and limiting process in Eq. (1.6) must not be interchanged, which imply to me that if we did ...
49 views

### Matrix representation of squeezing operator

In quantum mechanics we know that every operator can be represented by a matrix.Being a beginner of quantum optics, my question is does there exist a matrix for squeezing operator also? If does, can ...
40 views

185 views

### Why does separating variables in the spherically-symmetric TISE work?

When solving the one-particle Schrodinger equation for a spherically symmetric potential, we use the substitution $$\psi(r,\theta,\phi) = R(r)Y_l^m(\theta,\phi)$$ in order to solve. However, I am ...
33 views

28 views

### Are elements of different invariant subspaces of a self-adjoint set orthogonal?

I know that self-adjoint operators have orthogonal eigenspaces, but how does that generalize to the orthogonality of invariant subsapces? I am reading Fonda's Symmetry Principles in Quantum Physics ...
### Lie algebra with $\sim \!N^3$ generators [closed]
Is there a Lie algebra whose number of generators scales as $N^3$, or in general $N^p$ with $p$ an arbitrary positive integer? All the familiar examples, such as $\mathrm{U}(N)$ or $\mathrm{SU}(N)$ or ...