Expectation Value & Operator in Quantum Physics

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AshutoshTiwari358

The Modern Physics, Expectation Value & Operator in Quantum Physics

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Energy operator is
The energy for a system can be written as
Which can be in exchange by the terms of & .

Expectation Value & Operator in Quantum Physics

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The postulates of quantum mechanics have been successfully used for deriving exact solutions to Schrodinger equation for problems like  A particle in 1 Dimensional box  Harmonic oscillator  Rigid rotator  Hydrogen atom • However for a multielectron system, the SWE cannot be solved exactly due to inter-electronic repulsion terms. The SWE is solved by method of seperation of variables. • However, the inter-electronic repulsion term cannot be solved because the variables cannot be seperated and the SWE cannot be solved. • Approximate methods have helped to generate solutions for such and even more complex real quantum systems. • Approximate methods have been developed for solving Schrodinger equation to find wave function and energy of the complex system under consideration. • Two widely used approximate methods are, 1. Perturbation theory 2. Variation method Perturbation theory is an approximate method that describes a complex quantum system in terms of a simpler system for which the exact solution is known. • Perturbation theory has been categorized into, i. Time independent perturbation theory, proposed by Erwin Schrodinger, where the perturbation Hamiltonian is static. ii. Time dependent perturbation theory, proposed by Paul Dirac, which studies the effect of time dependent perturbation on a time independent Hamiltonian H0. PERTURBATION THEOREM FIRST ORDER PERTURBATION THEORY FIRST ORDER ENERGY CORRECTION FIRST ORDER WAVE FUNCTION CORRECTION APPLICATIONS OF PERTURBATION METHOD SIGNIFICANCE OF PERTURBATION METHOD

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