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	Title+Summary	Name	Date
	[LECS/QM-08002] Angular Momentum Eigenvalues Eigenvectors Node id: 6116page 1 Lets recall and discuss 2 Choose an orthonormal basis. 3 Use positivity of \(J_+ J_−\) and \(J_− J_+\) to get bounds on μ 4 \(J_+\) is a raising operator for \(J_z\) 5 \(J_−\) is a lowering operator for \(J_z\) 6 The difference between the maximum and minimum values of μ is an in teger 7 The results 8 Summary	kapoor	24-03-24 04:03:23	n
	[LECS/QM-08003] Application of Harmonic Oscillator to Crystals Node id: 6117page	kapoor	24-03-21 06:03:39	n
	[LECS/QM-08001] Energy Levels of Harmonic Oscillator Node id: 6115page CONTENTS Let us recall Operator algebra for harmonic oscillator Eigenvalues of N are non negative The operator a lowers the eigenvalues of N The eigenvalues of N are all non negative integers Properties of eigenvectors	kapoor	24-03-21 06:03:59	n

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