4.6. Consider a particle with total energy E subject to the following potential:

Question

4.6. Consider a particle with total energy E subject to the following potential: U3 The following questions refer to the solutions of the time-independent Schrodinger cquation for the above potential. (Note that U> U0.) a) For what ranges of energy will the wave function be localized, or delocalized? b For what ranges o energy will the particle have i) discrete or ii) continuous values of total energy L? c) Give both the classical and quantum mechanical probabilities (cither 0:or0 andU C. incident from the right with UE D. incident from the right with USE

Explanation / Answer

a) when E> U3 then wave function is delocalized. when E< U2, U3 then wave function is localized in 0<x<a and a<x<b

b) when E> U3, then it has continuous spectra and when E< U3, U2, it has discrete spectra.

c) (A) complete reflection (1; >0) (B) both reflection and transmission (1; >0) (C) complete reflection (1; >0), tunneling will happen (0; >0) (D) complete reflection (1; >0), tunneling will happen (0; >0)(E) both reflection and transmission (1; >0)

d) decaying

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