Question I: Consider a particle of mass m in a box of size L so the wave function vanishes at x=±L/2.
Find an upper bound E∗ on the ground state energy Egs using a simple trial wavefunction: a quadratic function of x which vanishes at ±L/2.
Useful integral:(limit 0 to 1) ∫(1-u2)^2du=8/5.
Egs (less than or equal) E∗ = ??
Compare the bound E∗ with the exact ground state energy E0:
E*/E0 =???
Querstion II: Consider a particle of mass m in a box of size L so the wave function vanishes at x=±L/2.
Use the uncertainty principle to calculate a lower bound on the ground state energy (Hint: assume the maximum possible value for Δx is Δx=L/2.)
Egs≥ ??