# 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 ...

Temperature of a system is defined as $$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$ Where $\Omega$ is the number of all accessible states (ways) for the system. $... 2answers 134 views ### Particle in a one dimensional box conditions Why does the wave function have to be$C^1(\mathbb{R})$for a finite square well but not for an infinite square well? For an infinite square well with boundaries at$x=0$and$x=L$, we have ... 3answers 128 views ### Can one construct a new operator in terms of the powers of another operator? Suppose we have a quantum state, well described by its time-independent wave function Psi. And we have a well-defined Hermitian (self-adjoint) operator$A$. We successfully evaluate the expectation ... 2answers 290 views ### Separation of variables in various PDEs, physical meaning The method of separation of variables produces an undetermined separation constant and a family of solutions indexed by the values of this constant. For instance, in the case of an infinitely long ... 2answers 144 views ### In QM, do we deal with basis or orthonormal sets? Most textbooks say, that given a (countable) basis${|\phi_n\rangle}$of a Hilbert space, that every vector$|\psi\rangle$of the space can be written as: $$\psi\rangle=\sum_{n=1}^\infty ... 1answer 266 views ### Could two different bases of a Hilbert space have different cardinality? [duplicate] Here is a quote from http://en.m.wikipedia.org/wiki/Hilbert_space#Hilbert_dimension (accessed: Nov. 22, 2013) : As a consequence of Zorn's lemma, every Hilbert space admits an orthonormal basis; ... 0answers 79 views ### Books for learning Mathematics in Physics? [duplicate] Currently I'm doing Advanced Classical Mechanics courses. I'm finding it hard to understand due to the lack of knowledge in linear algebra, multi variable calculus and other chapters. Can anyone ... 1answer 172 views ### Problem in Hamiltonian I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation$$ \hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ ... 1answer 45 views ### Thermofluid mechanics inclined plane As shown in the attacked image, a tank has an inclined wall at an angle of 450 to the horizontal. On this wall, there is a 1m square door that is hinged at A and has a simple latch at B. The distance ... 1answer 44 views ### A series of bound states covering an interval Generally, the bound states (normalizable eigenvectors) of a Hamiltonian have discrete eigenvalues. Is it possible for the eigenvalues to cover an interval? Say,$(a,b)$? That is, for each$E \in ...
Provided that the notion of "$\mbox{spacelike}$"-ness (of an interval) is symmetric: $$\text{spacelike}( \, x - y \, ) \Longleftrightarrow \text{spacelike}( \, y - x \, ),$$ then for any set $X$ (of ...