For an infinite square well from \(0\) to \(L\), what boundary conditions must the spatial wave function satisfy?

Find the allowed wave numbers for a particle in an infinite square well of width \(L\).

Write the normalized eigenfunction \(\psi_n(x)\) for a particle in a one-dimensional infinite well from \(0\) to \(L\).

Derive the energy levels for a particle of mass \(m\) in an infinite square well of width \(L\).

What is the ratio \(E_4/E_1\) for a particle in a one-dimensional infinite well?

How many interior nodes does the \(n=5\) state have in a one-dimensional infinite well?

Find the de Broglie wavelength of the \(n\)th state in a box of width \(L\).

A particle in a box emits a photon when it changes from \(n=3\) to \(n=1\). Find the photon energy in terms of \(E_1\).

Find \(\langle x\rangle\) for any stationary state in an infinite well from \(0\) to \(L\).

For the \(n\)th stationary state in a box, find \(\langle p\rangle\) and \(\langle p^2\rangle\).

For the ground state \(\psi_1=\sqrt{2/L}\sin(\pi x/L)\), find the probability of locating the particle in the middle half of the box.

Why is \(n=0\) not an allowed state for a particle in an infinite square well?

If the width of a box is doubled, how do all energy levels change?

If the particle mass is doubled while \(L\) is fixed, how do the box energy levels change?

A box state is \((\psi_1+\psi_2)/\sqrt2\). Is it an energy eigenstate? Explain.

For \(\psi=(\psi_1+\psi_2)/\sqrt2\) in a box, find the angular frequency of oscillation of the interference term in \(|\psi(x,t)|^2\).

Show that the normalized box eigenfunctions are orthogonal for different quantum numbers.

Compare an infinite well and a finite well of the same nominal width. Which has lower bound-state energies, and why?

A box has width \(L\). Find the frequency of a photon emitted in the transition \(n=2\to n=1\).

Prove that the ground-state energy of an infinite well cannot be zero without using the energy formula directly.