Commutative and non Commutative operators in Quantum Mechanics along with Solved Numerical Problems

Quantum Chemistry Lecture 1:

What is Quantum Mechanics? Why classical mechanics failed? Applications of Quantum Mechanics

Quantum Chemistry Lecture 2:

Difference between Quantum Mechanics and Classical Mechanics

Quantum Chemistry Lecture 3:

Heisenberg Uncertainty Principle

Quantum Chemistry Lecture 4:

De Broglie Hypothesis | Wave and Particle nature of matter

Quantum Chemistry Lecture 5:

Applications and Significance of Schrodinger Wave Equation

Quantum Chemistry Lecture 6:

What is wave Function? What does it tell us? Born interpretation of wave Function | Probability of finding a particle

Quantum Chemistry Lecture 7:

Eigen Functions and Eigen values along with Examples

Quantum Chemistry Lecture 8:

What is *Normalization* of wave function? *Why* the wave function should be normalized? *Significance* of Normalization

*Numerical Problems* on Normalization of wave function

Quantum Chemistry Lecture 9:

*Orthogonality* of wave function and *orthonormal* wave function with *Numerical Problems*

Quantum Chemistry Lecture 10:

What are operators in Quantum Mechanics and How to use them?

Quantum Chemistry Lecture 11:

Algebra of Operators in Quantum Mechanics | Properties | Addition subtraction and Multiplication

Quantum Chemistry Lecture 12:

Commutative and Non Commutative Operators with solved Problems

Quantum Chemistry Lecture 13:

Rules for writing an operator

Quantum Chemistry Lecture 14:

Hermitian Operator in Quantum Mechanics

Quantum Chemistry Lecture 15:

Properties of Hermitian Operator

Quantum Chemistry Lecture 16:

Second Property:

*Eigen Functions of Hermitian Operator corresponding to different Eigen Values are orthogonal*

Quantum Chemistry Lecture 17:

Prove that the operator for linear momentum is Hermitian

Quantum Chemistry Lecture 18:

Prove that the kinetic Energy operator is Hermitian Operator

Quantum Chemistry Lecture 19:

if two operators are Hermitian then their product is also Hermitian if they commute

Quantum Chemistry Lecture 20:

Postulates of Quantum Mechanics

Quantum Chemistry Lecture 21:

Time independent Schrodinger wave equation

Quantum Chemistry Lecture 22:

Steady state schrodinger wave equation

Quantum Chemistry Lecture 23:

Conclusion of particle in one dimensional box:

Quantum Chemistry Lecture 24:

Conclusion of particle in one dimensional box

[shubhajit_ghosh]

Sir please solve my following question:

If a and b are two commutating hermitian operators, and ψ1 and ψ2 are eigen functions of a with a1 and a2 eigen values respectively, then show that

Integration ψ1 b ψ2 = 0 (unless a1 = a2).

Sir please reply to my question it is very needful to me. Thank you sir.

[savithas]

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