respect to the variational parameter Denote by the value at this
minimum:This result for is higher than the exact eigenvalue.
5.32 Linear Potential I (Tennessee)
The potential V is symmetric. The ground state eigenfunction must also
be symmetric and have no cusps. A simple choice is a Gaussian:
where the variational parameter is andA is a normalization constant.
Again we must evaluate the three integrals in (A.3.1)–(A.3.4):
The minimum energy is found at the value where the energy derivative
with respect to is a minimum:
QUANTUM MECHANICS 279