A particle of mass m that is moving along the r-axis is experiencing a restoring force of the form F = -kfx, where k; is the spring constant. The Hamiltonian for this system is given as: +ksz 2m dr?' 2 The first two eigenstates of this system are given as: mkf Ae 1/4 mkf те where A and B are constants.
A particle of mass m that is moving along the r-axis is experiencing a restoring force of the form F = -kfx, where k; is the spring constant. The Hamiltonian for this system is given as: +ksz 2m dr?' 2 The first two eigenstates of this system are given as: mkf Ae 1/4 mkf те where A and B are constants.
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a) Show that ψν=1 is an eigenfunction of the Hamiltonian, and determine the energy of this state.
b) Is ψν=0 an eigenfunction of the momentum operator? How can you interpret your answer?
c) Are the functions ψν=0 and ψν=1 orthogonal?
d) In a given scenario, the restoring force F is getting weaker. What is the implication for the energy difference ∆E between consecutive states?
Transcribed Image Text:A particle of mass m that is moving along the r-axis is experiencing a restoring
force of the form F = -kfx, where k; is the spring constant. The Hamiltonian
for this system is given as:
+ksz
2m dr?' 2
The first two eigenstates of this system are given as:
mkf
Ae
1/4
mkf
те
where A and B are constants.
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