Calculate a lower bound on the ground state energy

Reference no: EM13720884

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≥ ??

Reference no: EM13720884

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