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hw3_phy4221

# hw3_phy4221 - PHY4221 Quantum Mechanics I Fall term of 2004...

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PHY4221 Quantum Mechanics I Fall term of 2004 Problem Set No.3 (Due on November 1, 2004) 1. A particle of mass m is in the ground state of the in fi nite square well. Suddenly the well expands to twice its original size – the right wall moving from L to 2 L – leaving the wave function (momentarily) undisturbed. The energy of the particle is now measured. (a) What is the most probable result? What is the probability of getting that result? (b) What is the next most probable result, and what is its probability? (c) What is the expectation value of the energy? Hint : If you fi nd yourself confronted with an in fi nite series, try another method. 2. What are the energy levels and the eigenfunctions for a potential of the form V ( x ) = ( , for x 0 1 2 2 x 2 , for x > 0 . Hint : This requires some careful thought, but very little actual computation. 3. Solve the time-independent Schrodinger equation for a centered in fi nite square well with a delta-function barrier in the middle: V ( x ) = ( αδ ( x ) , for | x | L , for | x | L .

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hw3_phy4221 - PHY4221 Quantum Mechanics I Fall term of 2004...

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