(a)
The energy of the particle in terms of
(a)
Answer to Problem 55P
The energy of the particle in terms of
Explanation of Solution
Write the Schrodinger’s equation.
Here,
Write the equation for the potential energy.
Here,
Write the expression of the given wavefunction.
Take the derivative of the above wave function with respect to
Take the derivative of the above equation with respect to
Put equations (II), (III) and (IV) in equation (I) and rearrange it.
Equation (V) will be true for all
Write the equation for the reduced Planck’s constant.
Here,
Conclusion:
Put equation (VII) in (VI).
Therefore, the energy of the particle in terms of
(b)
The normalization constant
(b)
Answer to Problem 55P
The normalization constant
Explanation of Solution
The given wavefunction is an even wavefunction.
Write the normalization condition for the given even wave function.
Put equation (III) in equation (VIII) and rearrange it.
Integrate the above equation.
Rearrange the above equation for
Conclusion:
Therefore, the normalization constant
(c)
The probability that the particle is located in the range
(c)
Answer to Problem 55P
The probability that the particle is located in the range
Explanation of Solution
Write the equation for the probability that the particle lies in the range
Here,
Put equation (III) in equation (IX) and rearrange it.
Integrate the above equation.
Conclusion:
Substitute
Therefore, the probability that the particle is located in the range
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Chapter 28 Solutions
Principles of Physics
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