Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 5.2, Problem 5.16P
To determine

The energy and degeneracy of the ground state of lithium (Z=3).

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Problem 10.1 Consider an electron in a circular orbit around a proton. As- sume the angular momentum can only take on values equal to nh where n is an integer (n=1,2,8,..) and ħ is a constant. Determine the possible values of the radius for the orbit and the possible values for the total energy. Make up a table of the energy for the first four energy states (that is, for the electron in the four smallest orbits).
The simple mass on a spring is the basis for our description of almost any oscillation. Let’s consider the vibrational states of a simple diatomic molecule, say N2. We will model it as two identical masses connected by a spring as shown in the figure at the top right.This is a little different from the cart on a spring since there is no wall -- both of the atoms are moving. But if we only look at oscillations of the molecule where the center of mass is not moving, the atoms are moving equally and oppositely. When one is going left, the other goes an equal amount to the right and vice versa. This is like two carts attached to a wall and oscillating equally and oppositely as shown in the lower picture. The only difference is the way we treat the spring. When each atom moves a distance x, the spring between the atoms actually stretches a distance 2x, so the force on each atom is -2kx. We can therefore model the motion of one of the nitrogen atoms as a single “cart on a spring” if we…
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