Electron in a Potential Rectangular Box k-Space

We are looking for a solution of the three-dimensional time-independent Schrb-dinger equation, 

The energy of the electron can take only discrete values. They are given by 

The n values can again be interpreted as quantum numbers which define energetic states of the electron and therefore determine the allowed values of energy. It can be seen from (2.48) that the values of k and n are closely related. 

Quantum numbers of the electron in the ground state are equal to 1,1,1 corresponding energy ofthe electron equals to The first excited state of the 

The three-dimensional time independent Schrodinger equation (2.44) has a family solutions of the (2.46) type. Every solution has corresponding wave vector k with components kx,ky, k given by (2.48). The k vectors constitute a vector space called fe-space (reciprocal space and phase space are other terms used in the hterature). The concept of k-space is extremely useful by considering the interaction of a radiation with a matter. 

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