Tagged Questions

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 ...

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Is there a general theorem stating why the restricted Lorentz group's exponential map is surjective?

The exponential map for the restricted Lorentz group is surjective. An outline of why is shown on the wiki page Representation Theory of the Lorentz Group. Is there a more general theorem that states ...
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Simulating of Fraunhofer Diffraction of Zigzags by FFT

I tried to study the diffraction pattern of the following zigzag grating by Matlab(FFT of this image).. And the result showed like this(please ignore the scale bar in this img) I think the ...
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Derivation of the Lippmann-Schwinger equation

I was trying to understand the derivation of the Lippmann-Schwinger equation in Sakurai's Modern Quantum Mechanics, Section 6.1. Our teacher presented a much simpler derivation, similar to that on ...
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How does the Hermiticity of an operator imply that functions have an expansion in in multiple bases?

In Shankar QM it is stated that since the $\boldsymbol K$ operator is Hermitian, vectors, which are expanded in the $\boldsymbol X$ basis with components $f(x) = \langle x | f \rangle$, must have an ...
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We start from an abstract state vector $\newcommand{\ket}[1]{|{#1}\rangle} \ket{\Psi}$ as a description of a state of a system and the Schrödinger equation in the following form $$\... 2answers 76 views What relative masses are required for them to collide n times in this scenario? Consider two masses, m and M, where M>m. They begin at rest on an infinite frictionless surface that is flat in one direction and sloped in the other direction. Mass m is placed a little bit up the ... 0answers 36 views QM scattering in a finite-sized box Background Consider a non-relativistic particle in a one-dimensional box of length L with (for definiteness) an attractive delta function at the origin: H = \frac{P^2}{2m} -|c|\delta(x), \qquad 0&... 2answers 182 views How much does it cost to become a theoretical physicists? [closed] Does becoming a theoretical physicist require a huge amount of money? Does theoretical physics require the same resources as mathematics: just papers and pencil? 2answers 106 views What is the wave propagated away from an impulsively excited spherical shell? Consider a spherical shell of radius R centered on the coordinate origin, and an impulsive excitation \delta (t) distributed over its surface ('ie. a single layer'). Each point on the sphere’s ... 2answers 141 views Identifying irreps of SU(2) How does one verify that, the representations of SU(2) corresponding to j=1/2 or j=1 is irreducible? I think showing the irreducibility (taking the representative matrices into a block-diagonal ... 2answers 985 views Nonseparable Hilbert space What kind of things can go wrong if we try to do quantum mechanics on a nonseparable Hilbert space? I have heard that usual mathematical manipulations that we take for granted will no longer hold. ... 1answer 173 views Applications of partial differential equations in material science [closed] I've been asked to find a partial differential equation that has applications in material science. However we are not allowed to use the heat equation. I have found Fick's laws (basically the heat ... 2answers 333 views Ambiguity in number of basis vectors [duplicate] The dimension of the Hilbert space is determined by the number of independent basis vectors. There is a infinite discrete energy eigenbasis \{|n\rangle\} in the problem of particle in a box which ... 3answers 337 views About the postulates of quantum mechanics and self-adjointness I am a freshman trying to understand the very basics of quantum mechanics but I met barriers at the beginning. What really matters is the postulates of quantum mechanics and their relationship with ... 2answers 133 views How can projection operators be expressed in form \frac{1}{d} (I + \sum_i r_i \lambda_i)? How can projection operator be expressed in form \frac{1}{d} (I + \sum_i r_i \lambda_i)? I was reading a paper and found out that the density matrix in d-dimensional Hilbert Space can be ... 1answer 153 views Must the wavefunction be analytic? In order to show the preservation of normalization of the wave function (in one dimension for now), one shows that the time differential is zero, which entails the following step:$$ \frac{d}{dt}\...
I have already asked this on the mathematics Stack exchange but I thought I'd try it here too! The Hodge star operator $\star$ is a linear map between $\bigwedge ^pV$ and $\bigwedge ^{n-p}V$ for an ...