An election is moving in the potential, U(x), shown to the right. This potential

Question

An election is moving in the potential, U(x), shown to the right. This potential is an even function of x. The energies, E1 = -1.5 eV and E2 = +0.5 eV, of the two lowest energy states are indicated by the dashed lines. Five x values are labeled A-F in the figure, Psi1(x) is the wave function of the ground state, and Psi2(x) is the wave function of the first excited state. Which one of the following statements is not true? Psi1(A) = Psi1(F) dPsi1/dx|r = C = 0 Psi2(A) = Psi2(F) d|Psi2|2/dx|r 0 Both Psi1 and Psi2 have exponential x dependence in the region B F? Psi1 Psi2 They are the same. If the system is prepared in a superposition of Psi1 and Psi2, at what frequency does the probability density oscillate? f = 4.8 times 1014 Hz f = 3.6 times 1014 Hz f = 1.24 times 1014 Hz

Explanation / Answer

(a)

  2(x) is the wave function of the first excited stateis the wave function of the ground state.

  2(x) is the wave function of the first excited state.

Wave function in First excited stae at A and F will be different.

(c)2(A)=2(F) ;it is not true

(b)

Wave function penetrates farther into the region x > F is the wave function of first excited state.

That is, for which wave function is (x) / (F)larger when x > F

= (b)   2

(c)

Energy after superposition=1.5+.5= 2eV

E=hf/e

f=(2*1.6*106-19)/(6.626068 × 10-34 )

=4.82*10^14 Hz or 4.8*10^14 Hz

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