(a)
The wave-function of the particle.
(a)
Answer to Problem 21P
Thewave function of the particles is
Explanation of Solution
Given:
The particle is constrained to move in the two dimensional region defined by,
Formula used:
The expression for Schrodinger equation in two dimensionis given by,
Calculation:
Theexpression for Schrödinger's equation with separation of variables for the term
Theexpression for Schrödinger's equation with separation of variables for the term
The above familiar differential equations have the usual solution,
Applying the boundary conditions,
Which implies it will have solutions,
Here,
Therefore the wave function corresponds for the state
Conclusion:
Therefore,the wave function of the particle is
(b)
The energy corresponding to the wave function.
(b)
Answer to Problem 21P
The energy corresponding to the wave function are
Explanation of Solution
Calculation:
The
Solving with the corresponding wave function,
The
Conclusion:
Therefore,the energy corresponding to the wave function are
(c)
The quantum numbers of the two lowest states that has degeneracy.
(c)
Answer to Problem 21P
The quantum numbers of the two lowest states that has degeneracy are
Explanation of Solution
Calculation:
The energy for the state
The energy for the state
Conclusion:
Therefore,the quantum numbers of the two lowest states that has degeneracy are
(d)
The quantum numbers of the three lowest states that has degeneracy.
(d)
Answer to Problem 21P
The quantum numbers of the three lowest states that has degeneracy are
Explanation of Solution
Calculation:
The state will have three fold degeneracy are
The energy for the state
The energy for the state
The energy for the state
Conclusion:
Therefore,the quantum numbers of the three lowest states that has degeneracy are
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Chapter 35 Solutions
Physics for Scientists and Engineers, Vol. 3
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