Operator formalism in Quantum mechanics
Operator formalism in Quantum mechanics
Introduction of Operator and Commutation relation
These are the p...}
Operator formalism in Quantum mechanics
Commutation Relation between position and linear momentum
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Commutation Relation between position and linear momentum$$[\hat y, \hat P_y]=i\hbar$$<...}
Operator formalism in Quantum mechanics
Commutation relation between different components
- \([\hat x, \hat H] = i\hbar \frac{\hat P_x}{m}= i\hbar \frac{\partial \hat H}{\part...}
Operator formalism in Quantum mechanics
Commutation relation between position and angular momentum, linear momentum and angular momentum, components of angular momentum operators.
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$$[\hat z, \hat L_x]= \hat y i\hbar, [\hat z, \hat L_y]= -\hat x i\hbar, [\hat z, \hat...}
Operator formalism in Quantum mechanics
Square of angular momentum operator, Ladder operator and some numerical examples
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$$[\hat L^2, \hat L_z] =0$$
Hence square of angular momentum and component of an...}
Operator formalism in Quantum mechanics
Hermitian Operators
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All the obserable quantities in Quantum Mechanics are associated with corresponding ope...}
Operator formalism in Quantum mechanics
Proof associated with Hermitian Operator
\((a) \hat P_x = -i\hbar \frac{\partial }{\partial x}\) is Hermitian operator.
Operator formalism in Quantum mechanics
Properties of Hermitian operator
Properties of Hermitian operator.
(1) Sum of any two like Hermitian is also...}
Operator formalism in Quantum mechanics
Properties of parity operator and Hermitian operator
Properties of parity operator \((\hat\pi\)):
(1) The eigen values of parity oper...}
Operator formalism in Quantum mechanics
Equation of motion in Quantum Mechanics
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Time dependent Schrodinger equation.
$$\hat H \psi= i\hbar \frac{\partial...}