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Quantum Mechanics , Schrodinger equation

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Could some please give detailed solutions to the following past paper Question 3.
Please highlight where standard formulas (showing the formulas in bold) are used and make all methods clear explaining what has been done and why.

See the attached file.

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Solution Summary

The solution contains detailed explanation of the various concepts of Quantum mechanics in solving problems related to the Schrodinger equation, Kinetic energy, wave functions, eigen functions of commuting operators, expectation value etc.

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