Unformatted text preview: 3. A particle of mass m interacts with a central potential deﬁned by V ( r ) = gδ ( ra ) where g and a are positive constants. Solve all the energy eigenfunctions of the system with zero orbital angular momentum. 4. The wave function of a particle is given by, ψ ( ~ r ) = A ( r + x ) eαr where A is a normalization constant, and r = p x 2 + y 2 + z 2 is the radial distance. It is given that Y 00 = 1 √ 4 π , Y 10 = r 3 4 π cos θ, Y 11 =r 3 8 π sin θe iφ ,Y 1 ,1 =Y * 11 . (a) Express the wave function in terms of spherical harmonics. (b) What is the expectation value of L 2 ? (c) If the zcomponent of the angular momentum is measured, what are the possible outcomes and the corresponding probabilities? 1...
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 Spring '11
 CFLO
 Energy, Mass, Work, Fundamental physics concepts, orbital angular momentum, θ

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