Quantum Mechanics - Infinite Potential Well

The figure above shows one of the possible energy eigenfunctions ψ(x) for a particle bouncing freely back and forth along the x-axis between impenetrable walls located at x = −a and x = +a. The potential energy equals zero for |x| > a. If the energy of the particle is 2 electron volts when it is in the quantum state associated with this eigenfunction, what is its energy when it is in the quantum state of lowest possible energy? 

A. 0 eV
B. 1/√2 eV
C. 1/2 eV
D. 1 eV
E. 2 eV

(GR8677 #90)

Solution:

Impenetrable walls = infinite potential walls.
The initial wavefunctions for the first four states in the system:

So, 

represents n = 2.

The energies for infinite potential walls:  E_n = n² E₁

Since E₂ = 2 eV → 2² E₁ = 2 → E₁ = 2/4 = 1/2 eV

Answer: C