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Unformatted text preview: Problem Set 11 Note: This problem set is due Nov 29 before midnight. Please leave it in my mailbox located at the first floor of Rutherford building. 1. A quantum particle of mass m is trapped inside two potential walls of infinite heights, and two potential steps of finite heights V and V 1 such that V 1 > V (see figure below): V(x) X L 1 L 2 L 3 V V 1 where L i denote the distances by which the potential steps are separated. Find the quan- tisation condition for the particle of energy E with the following three limits on E : ( a ) E < V , ( b ) V < E < V 1 and ( c ) E > V 1 . Discuss also the cases where (a) L 3 → ∞ , L 1 , L 2 finite, and (b) ( L 2 , L 3 ) → ∞ , L 1 finite. 2. A variant of the ammonia problem, that we have discussed before, will be to assume that the plane of the hydrogen atoms forms a potential barrier that would prohibit the nitrogen atom to cross over classically. In the figure below: L L L 1 2 3 V we have denoted the potential barrier by a height V . The nitrogen atom is trapped in...
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