Quantum Numbers, Permissible Energy Levels, and the Wave Function

2 Quantum Numbers, Permissible Energy Levels, and the Wave Function 

Assume now that the particle moves inside a box which is in the origin of the coordinates systems with dimensions a, b, and c, along the x, y, and z axes respectively. Then (Eq. 16.4.7) must be zero for values of X less than zero and greater than a, from which we obtain  

The permissible energy levels are obtained by introducing Eqs 16.4.9 into Eq. 16.4.2  

Notice the importance of energy separability, Eq. 16.4.2, in solving Eq. 16.4.1. (Could it be solved if this were not the case ) 

The origin of the quantum numbers and quantized energy levels is the imposition of boundary conditions. In the absence of confinement, the energy is continuous. 

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