StudentShare solutions

# Quantum Oscillator Problem - Assignment Example

Nobody downloaded yet

## Extract of sample Quantum Oscillator Problem

Figure 6.11 shows a plot of the 10th excited state probability density, |ψ10|2. Mathematica has the Hermite polynomials built-in. The quantum oscillator wave functions are given in equation 6.57; these wave functions are not normalized. The α in these equations is 𝑚 𝜔ℏ(HW Problem 6.36 and in-class work). The argument of the Hermite polynomials in equation 6.57 is listed as “x” but you will want to use 𝑢 = √𝛼𝑥 as the argument when you are actually write down or program the Hermite polynomials.
(a) Write down the (un-normalized) wave function for the 10th excited state; you can write it in terms of α. Also write down the energy for this state (write this energy in terms ℏ and ω)?
This type of which energy act on the energy eigenstates of the harmonic oscillator potential producing a un-normalized state of higher or lower energy.
a± =1/√2m(~/i∂/∂x ± imωx)

A=- ℏ^2 d^2/
2mr^2d
(b) Plot ψ10 and |ψ10|2(use u rather than x for your independent variable); your |ψ10|2 plot should look like Figure 6.11.
(c) Normalize ψ10 (use u);
Normalization the stationary wave functions are r a 1 2 2 ψn (x) = 2n√π n! Hn (ax) e− a x 2 .The diodes are available in the normalized E24 ±1 % (BZX84-A), ±2 % (BZX84-B) and approximately ±5 % (BZX84-C) tolerance range. The series includes 37 breakdown voltages with nominal working voltages from 2.4Vto75 V.
(d) Find the probability that the electron is in the region −0.5 ≤ √𝛼𝑥 ≤ 0.5. Use 3 significant figures for these numerical answers.
(e) What is 〈𝛼𝑥2〉 for this excited state? ...Show more

## Summary

Mathematica has the Hermite polynomials built-in. The quantum oscillator wave functions are given in equation 6.57; these wave functions are not normalized. …
Author : edwardomarvin
Read Text Preview
Save Your Time for More Important Things
Let us write or edit the assignment on your topic
"Quantum Oscillator Problem"
with a personal 20% discount.
Grab the best paper

### Check these samples - they also fit your topic

Quantum and Thermochemical Structure lap report
Introduction: The emission of electrons from metals irradiated by light was first observed by Becquerel in 1839. Under a classical model of light, one would expect the energy of the ejected electrons to be related to the intensity of the light waves used, and also that light waves of any frequency would be effective in ejecting electrons.
12 pages (3000 words) Assignment
Loaded Spring Oscillator, Hooke's Law
The phenomenon of simple harmonic motion is described by the motion of mass on a spring subjected to the linear elastic restoring force in accordance to Hook’s Law. It demonstrates a single resonant frequency and is sinusoidal in time. Through Fourier analysis technique the motion provides a basis for characterization of more complicated motions.
4 pages (1000 words) Assignment
Problem list
This variance becomes unfavorable if the actual costs are greater than the standard costs, and it implies that the company’s actual profits will be less than the
1 pages (250 words) Assignment
Part 1 - Loaded spring oscillator, Part 2 - Hookes Law
It demonstrates a single resonant frequency and is sinusoidal in time. Through Fourier analysis technique the motion provides a basis for characterization
4 pages (1000 words) Assignment
Problem discription
by the LCB students to upgrade their chances of getting employment after school such as taking part in other activities in the learning environment other than classwork. Such areas will help the students to add value to their knowledge by applying the principles they have
2 pages (500 words) Assignment
Problem Set
same point in pregnancy as or earlier than Marcelle, (b) at a later point in pregnancy than Marcelle, and (c) between their due date and the point at which Marcelle gave birth. Repeat the SPSS Connection from page 105 on your computer. Copy and paste the SPSS output for the
1 pages (250 words) Assignment
Problem set
This is a form of ambiguity and unnecessary prolixity. Such an answer was irrelevant, lacked order and was ludicrous. The humour comes to the idea of the biscuits being in the wrong place without explanation. The second issue is equally far
5 pages (1250 words) Assignment
Problem solving
Under the stare decisis doctrine, whenever a court decides to adhere to its principles, then it follows that the court has to make a ruling based on those principles
1 pages (250 words) Assignment
Financial problem
it is not a public listed Company then C and C hydraulics may decide to opt for IPO (Initial Public Offering) option to raise the capital in order to meet their fund requirements for the Company expansion into new sectors. This is the most effective mean to generate finance and
2 pages (500 words) Assignment
Problem
The study also observed that a sizeable portion of the heart disease cases is caused by hypertension. It is documented that racial and ethnic disparities exist in the toll of cardiovascular disease that results from hypertension. African Americans are affected more heavily
2 pages (500 words) Assignment
Hire a pro to write
a paper under your requirements!
Win a special DISCOUNT!
Put in your e-mail and click the button with your lucky finger
Your email
YOUR PRIZE:
Apply my DISCOUNT
Comments (0)
Click to create a comment
Contact Us