Question: 4. (a) Prove the following relation: [, sin(20)] = 2ih (sin - cos ) where is the azimuthal angle. (6) (b) A particle is

4. (a) Prove the following relation: [, sin(20)] = 2ih (sin -

4. (a) Prove the following relation: [, sin(20)] = 2ih (sin - cos ) where is the azimuthal angle. (6) (b) A particle is initially in its ground state in a one-dimensional harmonic oscillator potential, (x) V 1 =- 2 -kx2. If the spring constant is suddenly doubled, calculate the probability of finding the particle in the ground state of the new potential. (14) [20]

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