(a)
The expectation value of
(a)
Answer to Problem 57P
The expectation value of
Explanation of Solution
Write the equation for the expectation value of
Here,
Write the expression of the given wave function.
Write the expression for the complex conjugate of the given wave function.
Put equations (II) and (III) in equation (I) and rearrange it.
Integrate the above equation.
Conclusion:
Therefore, the expectation value of
(b)
The probability of finding the particle near
(b)
Answer to Problem 57P
The probability of finding the particle near
Explanation of Solution
Write the equation for the probability that the particle lies in the range
Here,
Put equations (II) and (III) in equation (IV) and rearrange it.
Integrate the above equation.
Conclusion:
Therefore, the probability of finding the particle near
(c)
The probability of finding the particle near
(c)
Answer to Problem 57P
The probability of finding the particle near
Explanation of Solution
Write the equation for the probability that the particle lies in the range
Put equations (II) and (III) in equation (IV) and rearrange it.
Integrate the above equation.
Conclusion:
Therefore, the probability of finding the particle near
(d)
The argument for the statement that the result of part (a) does not contradict the result of part (b) and part (c).
(d)
Answer to Problem 57P
It is more probable to find the particle either near
Explanation of Solution
Probability density is the relative probability per unit volume that the particle will be found at any given point in the volume. The probability density for the given function with
The expectation value of
Conclusion:
Thus, it is more probable to find the particle either near
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Chapter 28 Solutions
Principles of Physics: A Calculus-Based Text
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