Consider a particle of mass m in a box of size L so the wave function vanishes at x=±L/2.   Find an...

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  =???

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≥   ??