Question

The wave function of a particle of mass in in a unidimensional potential field U (x) = kx²/2 has in the ground state the form ψ(x) = A e^{-αx^2} , where A is a normalization factor and α is a positive constant. Making use of the Schrodinger equation, find the constant α and the energy E of the particle in this state.

Answer 1

since ψ≠0  the bracket must vanish identicall. This means that the coefficient of x² as well the term independent of x must vanish. We get