D'alembert for semi-infinite string (on R-)

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D'Alembert problem for semi infinite string on R-

utt=c2 uxx ( -\infty<x<0)

Initial condition:
u(x,0)=f(x)
ut(x,0)=g(x)

Boundary condition:
u(0,t)=0

please help me to solve it
 
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Start by assuming a separable form for the solution.
 

Thread 'Number of quantum accessible states of a particle given T, N?'

It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have...
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