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Quantization of energy

Since n can have only integral values equal to 1,2,3 etc, therefore from equation it follows that the energy E associated with the motion of a particle in a box can have only discrete values i.e., the energy is quantized.

n = 4          E4 =16h2/8ma2

n = 3          E3 = 9h2/8ma2

n = 2          E2 = 4h2/8ma2               

n = 1           E1 = h2/8ma2

The integer n is called the quantum number of the particle.

Further putting n=1,2,3.... tainted of the particle of mass m confined in the box of length a are shown in fig. It is important to noted that separation of energy levels also depends upon the box light a. As a increases, i.e., the space available to a particle increases, energy quanta become smaller and energy levels move closer together. If the box light becomes very large, quantization disappears and there is a smooth transition from quantum behavior to classical behavior. This is called correspondence principle given by Bohr.

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