Conceptual Questions

Can the magnitude of a wave function $({\text{Ψ}}^{*}\left(x,t\right)\text{Ψ}(x,t))$ be a negative number? Explain.

What is the physical meaning of a wave function of a particle?

If the formalism of quantum mechanics is ‘more exact’ than that of classical mechanics, why don’t we use quantum mechanics to describe the motion of a leaping frog? Explain.

Can we measure the energy of a free localized particle with complete precision?

What is the difference between a wave function $\psi (x,y,z)$ and a wave function $\text{Ψ}(x,y,z,t)$ for the same particle?

Explain the difference between time-dependent and -independent Schrӧdinger’s equations.

Using the quantum particle in a box model, describe how the possible energies of the particle are related to the size of the box.

For a quantum particle in a box, the first excited state $({\text{Ψ}}_2)$ has zero value at the midpoint position in the box, so that the probability density of finding a particle at this point is exactly zero. Explain what is wrong with the following reasoning: “If the probability of finding a quantum particle at the midpoint is zero, the particle is never at this point, right? How does it come then that the particle can cross this point on its way from the left side to the right side of the box?

Explain the connection between Planck’s hypothesis of energy quanta and the energies of the quantum harmonic oscillator.

Use an example of a quantum particle in a box or a quantum oscillator to explain the physical meaning of Bohr’s correspondence principle.

When an electron and a proton of the same kinetic energy encounter a potential barrier of the same height and width, which one of them will tunnel through the barrier more easily? Why?

Explain the difference between a box-potential and a potential of a quantum dot.

A tunnel diode and a resonant-tunneling diode both utilize the same physics principle of quantum tunneling. In what important way are they different?