(a)
Verify that given value of
(a)
Answer to Problem 37P
The value of
Explanation of Solution
Write the expression for normalization constant.
Substitute
Expand the above expression.
Conclusion:
For last two integrals, the integral value of both is same as the functions
Solve the last integral part using waveform.
Substitute 1 for
Thus, the value of
(b)
The value of function at any later time
(b)
Answer to Problem 37P
The function at any later time
Explanation of Solution
Write the expression for time dependent wave function.
Substitute
Conclusion:
Thus, the function at any later time
(c)
Verify that average energy in the superposition is the arithmetic mean of ground and first excited state energies.
(c)
Answer to Problem 37P
Superposition is not the stationary state but average energy in the superposition is the arithmetic mean of ground and first excited state energies.
Explanation of Solution
The stationary state of any function is defined by the Eigen function. A wave is in stationary state when it is an Eigen function of energy operator.
Write the expression for action of energy operator on function.
Write the expression for average energy.
Conclusion:
Substitute
Here,
Substitute
Thus, superposition is not the stationary state but average energy in the superposition is the arithmetic mean of ground and first excited state energies.
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Chapter 6 Solutions
Modern Physics
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