Equation for spectrum of electron states in a potential well with uneven bottom

A method is proposed to determine the spectrum of bound states of electron making a stationary motion in a three-dimensional quantum well with uneven bottom. It is shown that the problem of finding the energy eigenvalues is reduced to investigation of multichannel scattering of the particle from the internal part of potential. Equation for the energy, depending on the transmission and reflection amplitudes, is obtained. For illustration of application of the method to concrete systems, a three-dimensional asymmetric quantum well with uneven bottom is considered.