- Demonstrate that
- Verify that
- Let
be an operator whose eigenvalues
can take a continuous range of values. Let the
be the corresponding eigenstates. Let
be a function of
that can be
expanded as a power series. Demonstrate that
- Consider a Gaussian wavepacket whose corresponding wavefunction is
- Let
and
be operators that displace a
quantum mechanical system the finite distances
and
along the
- and
-directions,
respectively. Demonstrate that
- Suppose that we displace a one-dimensional quantum mechanical system a finite distance
along the
-axis. The
corresponding operator is
Let , and let denote an eigenket of the operator belonging to the eigenvalue . Demonstrate that