68111135-3-4-Application

# 68111135-3-4-Application - Commutator Algebra Here we...

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Commutator Algebra Here we illustrates commutator algebra using one dimensional quantum systems. When we work with the Schrödinger Equation or in any other formulation of Quantum Mechanics, exact values of properties can not be used. Instead we use operators. Mathematically, a commutator is written: Where [. .,. .] is commutator bracket. If the result of commutation is zero then we say the operators and commute. Otherwise these operators do not commute. The famous Heisenberg Uncertainty principle is a direct consequence of the fact that position and momentum do not commute; therefore we cannot precisely determine position and momentum at the same time. Construction of operators using postion and momentum operator: In order to construct quantum mechanical operators, first we write classical observable interms of momentum and position and then we substitute representation of postion and momentum operator. Example: Energy equation for the classical Harmonic oscillator is

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68111135-3-4-Application - Commutator Algebra Here we...

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