A one-dimensional harmonic oscillator has a force constant k and mass m. For Que

Question

A one-dimensional harmonic oscillator has a force constant k and mass m. For Questions 5 to 7, consider the four probability densities (a) to (b) shown below, obtained from four different solu- tions of the harmonic oscillator Schrödinger equation. Question 5 (5 points): Which of the above is the probability density for the n 3 vibrational state? a. Probability density (a) b. Probability density (b) c. Probability density (c) d. Probability density (d) e. All of the above f. None of the above Question 6 (5 points): Which of the above represents a state that is unlikely to be found at the equilibrium position? a. Probability density (a) b. Probability density (b) c. Probability density (c) d. Probability density (d) e. All of the above f. None of the above Question 7 (5 points): Which of the above represents a state where the average position of the particle is the equilibrium position? a. Probability density (a) b. Probability density (b) c. Probability density (c) d. Probability density (d) e. All of the above f. None of the above

Explanation / Answer

5)It is option (a)

as for SHO number nodes of a state=vibrational quantum number of that state.

6)it is option (f)

In case of SHO only in Ground state the probability density is maximum an with the gradual increase of vibrational quantum no. equilibrium probability density decreases and probabilty density increases towards the terminal points.Now every in every plot this criterion has been maintained.

7)it is option (e).

As all for all graphs average poition=o that is equilibrium posotion.This is the symmetric feature of all the above plots of the SHO.

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