Question: One classic problem in quantum mechanics is the harmonic oscillator. In this problem a particle is subjected to a one-dimensional potential (taken to be along

One classic problem in quantum mechanics is the “harmonic oscillator.” In this problem a particle is subjected to a one-dimensional potential (taken to be along x) of the form V (x) ∝ x², where −∞ ≤ x ≤ ∞. The probability distribution function for the particle in the lowest-energy state is:

P (x) = Ce^-ax2 / 2

Determine the expectation value for the particle along x (that is, x). Can you rationalize your answer by considering the functional form of the potential energy?

Step by Step Solution

★★★★★

3.51 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The last equality arises from x being an odd function whi... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Physical Chemistry Questions!

Assume that you are the president of Nuclear Company. At December 31, 2017, the end of the first year of operations, the following financial data for the company are available: Required 1. Prepare a...

A one-dimensional harmonic oscillator in a stationary state has (T) = 5.0 X 10-19 J. Find E and (V) for this state.

Classically, the average kinetic energy of the harmonic oscillator equals the average potential energy. We may assume that this is also true for the quantum mechanical harmonic oscillator. Use this...

The classical probability distribution function for a particle in a one-dimensional box of length L is P = 1/L. (a) Show that the classical expectation value of x 2 for a particle in a...

2. Approximation Methods (a) Perturbation Theory Consider a charged one-dimensional quantum harmonic oscillator (ID QHO) in a con- stant electric field along the x-axis of strength G. The charge on...

please help me solve these questions, the teacher included the final answer in the screenshots but I want the steps for it so I can understand how they got the final answer ( that's all screenshot so...

1. (80 pts) At the turn of the 19th and 20th centuries saw several groundbreaking progresses in physics. Quantum mechanics is one of the physical theories developed in this period, which have since...

Can I get the solution for these Atomic & Quantum Mechanics Physics problems? Textbook: Introduction to Quantum Mechanics, 2nd edition, by David J. Griffiths (Pearson Prentice Hall, Upper Saddle...

Solving ODE using python Please find the mistake in this code Thanks! Question 12: Consider the one-dimensional, time-independent Schroedinger equation describing a particle with wave function (x)...

Python please. Thanks!! Question 12: Consider the one-dimensional, time-independent Schroedinger equation describing a particle with wave function (x) and energy E : 2m2dx2d2(x)+V(x)(x)=E(x). Values...

please help, python Question 12: Consider the one-dimensional, time-independent Schroedinger equation describing a particle with wave function (x) and energy E : 2m2dx2d2(x)+V(x)(x)=E(x). Values for...

What are the pros and cons of measuring the success or failure of an acquisition by immediate stock price reactions to its announcement? When is this approach most likely to provide insights?

Use Galerkins method to develop an element equation for a steady-state version of the advection-diffusion equation described in Prob. 30.7. Express the final result in the format of Eq. (31.26) so...

Janet owns a home at the lake. She incurs the following expenses: Mortgage interest$ 1 , 3 0 0 Property taxes 8 0 0 Insurance 1 , 5 0 0 Utilities 1 , 8 0 0 Repairs 3 0 0 Depreciation 4 , 0 0 0...

Draw a graph to show the relationship between the price and the number of umbrellas purchased, holding the amount of rainfall constant at 200 mm. Describe this relationship.

Describe how the mean energy of a system composed of two levels varies with temperature.

Suggest a physical interpretation of the relation between pressure and the partition function.

Calculate the weight of the configuration in which 16 objects are distributed in the arrangement 0, 1, 2, 3, 8, 0, 0, 0, 0, 2.

What is the output of the following program when the method is called with 5? void unknown(int n) if (n>0) unknown(n-1); System.out.print("?"); a. ???? b. ????? c. ?????? d. None of the above

Part Quality Supplier Good Minor Defect Major Defect A 100 5 8 B 160 27 4 C 150 11Chi Square - Test of Independence ChiSquare - Test of Independence Question 20 (4 points) DATA contains Part Quality...

Cori's Meats is looking at a new sausage system with an installed cost of $475,000. This cost will be depreciated straight-line to zero over the project's five-year life, at the end of which the...