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5thquiz

# 5thquiz - h h h h h h(3 Comparing the result of equation(3...

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PHY4221 Quantum Mechanics I (Fall 2004) Quiz 5 (Answers) With the given tentative wave function, we could have: ( 29 ( 29 ( 29 ( 29 ( 29 2 0 2 2 dx x H x H A dx x x A A V m π -∞ -∞ Ψ Ψ = Ψ Ψ = - h (1) Using the variational principle then: ( 29 2 2 0 4 2 0 m V H A A A π = = h (2) And so the upper limit to the ground state energy is given as: 2 2 2 2 2 0 0 0 4 2 4 2 2 0 0 2 2 2 0 2 2 4 2 2 m V m V E V m mV mV mV π π π
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Unformatted text preview: h h h h h h (3) Comparing the result of equation (3) with the exact solution for delta potential well case: 2 2 2 exact mV E = -h (4) you will find that the variational result is larger than the exact solution, as expected....
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