Concept explainers
(a)
Show that
(a)
Answer to Problem 5.1P
It is proved that
Explanation of Solution
Given, the separation between the two particles is
The position of the center of the mass is
The reduced mass of the system is
Substitute equation (I) in (II) and solve for
Hence it is proved that
Similarly substitute equation (I) in (II) and solve for
Hence it is prove that
Let the coordinates of
Equation (I) and (II) with respect to
Substitute
Similarly equation (I) and (II) with respect to
Similarly equation (I) and (II) with respect to
Adding,
Hence it is proved that
Similarly for particle
Equation (I) and (II) with respect to
Substitute
Similarly equation (I) and (II) with respect to
Similarly equation (I) and (II) with respect to
Adding,
Hence it is proved that
Conclusion:
Thus, it is proved that
(b)
Show that the Schrodinger equation becomes
(b)
Answer to Problem 5.1P
It is proved that the Schrodinger equation becomes
Explanation of Solution
Write the Schrodinger’s time-independent equation for two-particle system
From part (a),
Since, from equation (III),
Hence it is proved that
Conclusion:
Thus, it is proved that the Schrodinger equation becomes
(c)
The one-particle Schrodinger equation of
(c)
Answer to Problem 5.1P
The one-particle Schrodinger equation of
Explanation of Solution
Write the one-particle Schrodinger equation
The one-particle Schrodinger equation for
The one-particle Schrodinger equation for
The total energy is
Hence it is proved.
Conclusion:
The one-particle Schrodinger equation of
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Chapter 5 Solutions
Introduction To Quantum Mechanics
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