Changes

<math>

<math>

\frac{d^2 \psi}{dx^2} = -k_0 \psi

\frac{d^2 \psi}{dx^2} = -k^2_0 \psi

</math>

</math>

<math>

<math>

\frac{d^2 \psi}{dx^2} = -k_1 \psi

\frac{d^2 \psi}{dx^2} = -k^2_1 \psi

</math>

</math>

This section has advanced mathematical concepts such as [[complex numbers]] and [[hyperbolic trigonometric functions]].

This section has advanced mathematical concepts such as [[complex numbers]] and [[hyperbolic trigonometric functions]].

First, We start from the split wavefunction above, remembering that we have already shown <math>F=0</math>. Then the continuity conditions of a wavefunction (the wavefunction and its first derivative must be continuous) to find four simultaneous equations:

First, We start from the split wavefunction above, remembering that we have already shown <math>F=0</math>. Then the continuity conditions of a wavefunction (the wavefunction and its first derivative must be continuous) to find four simultaneous equations: