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برق و الکترونیک::
حالت ویژه
The fact that application of boundary con- ditions to the wave equation gives rise to eigenstates is a direct consequence of the mathematical structure of the equation.
Because $n(r) 2d3r is simply the probability of finding a particle in state $n(r) in the volume element d3r at position r in space, it is also convenient to require that eigenstates $n(r) be normalized.
where kn nu/L is the wave vector and cn kk2/2m is the angular frequency of the n-th eigenstate (see Problem 3.6).
As discussed in Section 3.3.1, to find the eigenenergies and eigenstates of a particle of mass m in a one-dimensional rectangular potential well with infinite barrier energy the boundary conditions require $0(x0) $N (xN ) 0.
The current has an oscillatory time dependence, which in our particular example is given by the difference frequency, c2 c1, between the $1 and $2 eigenstates.
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