Bad Qubits — Learn Quantum by Doing

Multiple choice

For a particle of mass

m

in an infinite square well of width

L

, the allowed energy eigenvalues are

E_n = n^2 \pi^2 \hbar^2 / (2 m L^2)

for

n = 1, 2, 3, \dots

. What does this imply about the lowest possible energy?

The lowest energy $E_1$ is strictly positive (nonzero zero-point energy); the particle can never be at rest
The lowest energy is $E_0 = 0$ , so the particle can sit at rest at the bottom of the well
The lowest energy is negative, since the particle is bound inside the well
Energies form a continuous band, so arbitrarily small positive energies are allowed