PC 253: Quiz

Finding Roots Quiz

Consider the problem of a particle of mass m in a one-dimensional quantum well with the potential energy

Potential

Solving Schrödinger's equation leads to equations which must be solved to find the allowed energies E . For this problem, solving Schrödinger's equation gives the equation

Condition on Energies            (1)
where
kappa definition                        (2)
and
Definition of s                    (3)

Find the three lowest energy states of the system by numerically solving the equation (1) assuming the particle is an electron. The value of V 0 = 1.0 keV, and a = 0.529 × 10 -10  m.

HINT: Start by computing the dimensionless constant κ from equation (2), then numerically solve equation (1) for the allowed values of s . Finally, solve equation (3) for E , then use the computed value for κ and the allowed values of s to find the allowed values of E .