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Free particle Wave equation | Energy and momentum operator

July 11, 2018 by Dr. IM Leave a Comment

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What is the Free particle Wave equation?

Derive Energy and momentum operator with the help of Free particle Wave equation

Answer:

Free particle Wave equation:

If we assume that matter waves are produced due to variation in the wave function similarly as sound waves are produced due to variation in pressure and electromagnetic waves are produced due to variation in electric and magnetic fields. The wave function is a function of both the position and time. Now, let us assume that wave function for the wave moving along positive x-direction can be represented as

Free partical wave function

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Free partical wave function 1

This is the free particle wave equation.

Energy and momentum operator:

  • Energy operator

On partially differentiating with respect to t to equation (3), we get

Energy operator

  • Momentum operator

Momentum operator

This is known as momentum operator.

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Filed Under: Engineering Physics, Quantum Mechanics Tagged With: Energy operator, Free partical wave function, Momentum operator

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