Chapter 40: One-Dimensional Quantum Mechanics

Two adjacent energy levels of an electron in a harmonic potential well are known to be $2.0eV$ and $2.8eV$. What is the spring constant of the potential well?

An electron confined in a harmonic potential well emits a 1200nm photon as it undergoes a $3\to 2$quantum jump. What is the spring constant of the potential well?

The correspondence principle says that the average behavior of a quantum system should begin to look like the Newtonian solution in the limit that the quantum number becomes very large. What is meant by “the average behavior” of a quantum system?

An electron in a rigid box absorbs light. The longest wavelength in the absorption spectrum is$600nm$. How long is the box?

An electron in a harmonic potential well absorbs a photon with a wavelength of $400nm$as it undergoes a $1\to 2$ quantum jump. What wavelength is absorbed in a $1\to 3$ quantum jump?

An electron is confined in a harmonic potential well that has a spring constant of $12.0N/m$. What is the longest wavelength of light that the electron can absorb?

Use the data from Figure 40.24 to calculate the first three vibrational energy levels of a $C=O$carbon-oxygen double bond.

Verify that the n=1 wave function ${\psi }_1\left(x\right)$ of the quantum harmonic oscillator really is a solution of the Schrödinger equation. That is, show that the right and left sides of the Schrödinger equation are equal if you use the ${\psi }_1\left(x\right)$ wave function.

An electron approaches a $1.0\mathrm{nm}$ wide potential-energy barrier of height $5.0eV$. What energy electron has a tunneling probability of (a) 10%, (b) 1.0%, and (c) 0.10%?

What is the probability that an electron will tunnel through a $0.45\mathrm{nm}$gap from a metal to a STM probe if the work function is $4.0\mathrm{eV}$?