The particle cannot exits outside the box where the potential is infinite. Hence the wavefunction, <math>\psi</math>, here must be zero outside the box. Now let us consider inside the box. The Schrödinger equation inside the potential well becomes:
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The particle cannot exist outside the box where the potential is infinite. Hence the wavefunction, <math>\psi</math>, here must be zero outside the box. Now let us consider inside the box. The Schrödinger equation inside the potential well becomes:
<math>- \frac{\hbar^2}{2m} \frac{d^2 \psi}{dx^2} = E \psi</math>
<math>- \frac{\hbar^2}{2m} \frac{d^2 \psi}{dx^2} = E \psi</math>