Excuse me , anyone can solve this problem? 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 to1)∫(1−u^2)^2du=8/15. 1)Egs(=??

Question

Excuse me , anyone can solve this problem?
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 to1)∫(1−u^2)^2du=8/15.
1)Egs(<or=)E*    =??    2)E*/E0  =   ???
Also,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(assume the maximum possible value for Δx=L/2)Egs>=??

irishboy123 · Answer

you need to generate the Schrodinger wave equation W(x) using the suggested profile. 

subject to the normalisation consition that ∫ W^2 (x) dx = 1 between -inf and inf

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