where , , and are constants. Demonstrate that
where is the momentum conjugate to the position operator . Demonstrate that
[Hint: Use the momentum representation, .] Similarly, demonstrate that
Hence, deduce that
where is a general function of .
Let , and let denote an eigenket of the operator belonging to the eigenvalue . Demonstrate that
where the are arbitrary complex coefficients, and , is an eigenket of the operator belonging to the eigenvalue . Show that the corresponding wavefunction can be written
where for all .