Chapter 7, Problem 7E.17P

(a)

Interpretation Introduction

Interpretation:

The explanation as to why ${\langle x\rangle }_v=0$ for a harmonic oscillator has to be stated.

Concept introduction:

Expectation value is the average value of the large number of measurements of an observable.  The expectation value of a measurable parameter is calculated by the formula shown below.

  $\langle \Omega \rangle ={\displaystyle \int {\psi }^{*}\widehat{\left(\Omega \right)}\psi \text{d}\tau }$.

(b)

Interpretation Introduction

Interpretation:

The explanation as to why ${\langle p_x\rangle }_v=0$ for a harmonic oscillator has to be stated.

Concept introduction:

Same as mentioned in part (a).

(c)

Interpretation Introduction

Interpretation:

The expression for ${\langle p_x^2\rangle }_v$ for a harmonic oscillator has to be stated.

Concept introduction:

Same as mentioned in part (a).

(d)

Interpretation Introduction

Interpretation:

The expressions for $\Delta x$ and $\Delta p_x$ for a harmonic oscillator have to be stated.

Concept introduction:

Same as mentioned in part (a).

(e)

Interpretation Introduction

Interpretation:

The expression for the product of $\Delta x$ and $\Delta p_x$ for a harmonic oscillator has to be stated.  The validation of this expression for the Heisenberg uncertainty principle has to be shown.

Concept introduction:

Same as mentioned in part (a).

(f)

Interpretation Introduction

Interpretation:

The state that corresponds to minimum value of $\Delta x\cdot \Delta p_x$ for a harmonic oscillator has to be stated.

Concept introduction:

Same as mentioned in part (a).