2. (14 pts) A quantum particle with unit mass (m = 1) is in a one dimensional box where
energy, V (x) = o for o < x < 2 and V (x) = 80 otherwise. Answer the following
(a) (6/14) Prove that
on(x) = sin ( NTT ), n = 1,2,
is an eigenfunction of the Hamiltonian satisfying the
boundary condition, determine its eigen-
value, and the corresponding de Broglie wavelength.
(b) (8/14) particle is in a state
Given that the represented by the following wave function,
= 1 TTX 2 + 13 2
what are the expectation values of the energy and position measurements?
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