Theory of Quantum Phase Space and Rigorous Solution of Hydrogen Atom

The method of wave mechanics in the quantum phase-space representation established by TorresVega and Frederick is introduced.The "Fourier-like" projection transformation between phase-space representation and position or momentum representation is discussed.The rigorous solutions of stationary Schrdinger equation for one-dimensional hydrogen atom are obtained.It is described that the wave functions are not unique in phase space.