## Postulates Of Quantum Mechanics

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# Postulates of Quantum Mechanics

The derivation of the Schrodinger wave equation, as given in Section was based upon the concept that the electron has wave motion. However, the Schrodinger wave equation can be derived without making use of this concept but on the basis of certain postulates called the ‘postulates of quantum mechanics’. These are as follows:

(1) For every time independent state of system, a function of the coordinates can be written which is single valued, continuous and finite throughout the configuration space. This function describes completely the state of the system.

(2) To each observable quantity in classical mechanics, like position, velocity, momentum, energy etc. there corresponds a certain mathematical operator in quantum mechanics, the nature of which depends upon the classical expression foe the observable quantity. For example,

(i) The operator corresponding to a position co-ordinate multiplication by the value of that co-ordinate i.e. operator for a position coordinate x is the multiplier x.

(ii) The operation representing the momentum (p) in the direction of any co-ordinate q is the differential operator

Where h is Pluck’s content and

The significance of setting up and using the operator corresponding to a given observable may be understood as follows:

For example, the operator for linear momentum parallel to x=axis is

This means that to find the linear momentum of a particle parallel to the x-axis, we use the eigen value equation

i.e., we differentiate the wave function with respect to x and multiply the result with and then from the eigen value equation, we can know the value of the momentum P.

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(1) For every time independent state of system, a function of the coordinates can be written which is single valued, continuous and finite throughout the configuration space. This function describes completely the state of the system.

(2) To each observable quantity in classical mechanics, like position, velocity, momentum, energy etc. there corresponds a certain mathematical operator in quantum mechanics, the nature of which depends upon the classical expression foe the observable quantity. For example,

(i) The operator corresponding to a position co-ordinate multiplication by the value of that co-ordinate i.e. operator for a position coordinate x is the multiplier x.

(ii) The operation representing the momentum (p) in the direction of any co-ordinate q is the differential operator

Where h is Pluck’s content and

**.**The significance of setting up and using the operator corresponding to a given observable may be understood as follows:

For example, the operator for linear momentum parallel to x=axis is

This means that to find the linear momentum of a particle parallel to the x-axis, we use the eigen value equation

i.e., we differentiate the wave function with respect to x and multiply the result with and then from the eigen value equation, we can know the value of the momentum P.

For more help in

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