Development of time dependent and independent Schrodinger equation

Equation to be remember:

1. $$\therefore i\hbar \frac{\partial \psi(\vec r,t)}{\par...}

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Solution of Schrodinger equation

• Point and formula to be noted:

1. $$\therefore\;\; \phi(t)= \phi(0) e^...}

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Equation of continuity in quantum mechanics

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Equation of continuity in quantum mechanics

1. $$or,\;\; \frac{\partial }{\partial t}(\psi^*\psi)+\nabla\cdot\biggl[\frac{\hbar}{2im}[...}

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Step of Normalization

1. If \(\psi(r,t) \) does not satisfy the condition of normalization i.e.

   $$\iiint...}

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Importance of normalization

• To represent particle by wave packet, the amplitude of wave function should be fixed. (...}

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Eigen Value Equation

• $$=i\hat h\biggl[ \hat i\frac{\partial}{\partial x}+\hat j\frac{\partial}{\partial y}+\...}

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Expectation Value of dynamical Quantity:

• The average or expectation value of A over \(\psi(x)\) state is represented as, $$<...}
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Orthogonality of wavefunction and eigen value

1. Two wave function \(\psi_1(x)\) and \(\psi_2(x)\) are called orthonormal if they are or...}

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Example of Normalization

• $$\therefore \Delta x\cdot \Delta P_x=\frac{\hbar}{2}$$

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