Find the ground state of the quantum harmonic oscillator. Start by showing that the Hamiltonian from eq
Question:
Find the ground state of the quantum harmonic oscillator. Start by showing that the Hamiltonian from eq
can be ?factorized? similar to (a2 ? b2) = (a ? b)(a + b) in the form
Where?
Show that the Schr?dinger equation is satisfied if (? d/dx + x/?)?0(x) = 0. Show that ?0(x) = Ne?ax2 is such a solution for the right choice of a. Find N such that ?0(x) is normalized. What is the energy of this state?
Transcribed Image Text:
h2 d? 1 2m dx2 +kx 있) V(x) =D Ev (x)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 69% (13 reviews)
First show that the Hamiltonian given reduces to the harmonic oscillator Hamiltonian Next suppose dd...View the full answer
Answered By
JAPHETH KOGEI
Hi there. I'm here to assist you to score the highest marks on your assignments and homework. My areas of specialisation are:
Auditing, Financial Accounting, Macroeconomics, Monetary-economics, Business-administration, Advanced-accounting, Corporate Finance, Professional-accounting-ethics, Corporate governance, Financial-risk-analysis, Financial-budgeting, Corporate-social-responsibility, Statistics, Business management, logic, Critical thinking,
So, I look forward to helping you solve your academic problem.
I enjoy teaching and tutoring university and high school students. During my free time, I also read books on motivation, leadership, comedy, emotional intelligence, critical thinking, nature, human nature, innovation, persuasion, performance, negotiations, goals, power, time management, wealth, debates, sales, and finance. Additionally, I am a panellist on an FM radio program on Sunday mornings where we discuss current affairs.
I travel three times a year either to the USA, Europe and around Africa.
As a university student in the USA, I enjoyed interacting with people from different cultures and ethnic groups. Together with friends, we travelled widely in the USA and in Europe (UK, France, Denmark, Germany, Turkey, etc).
So, I look forward to tutoring you. I believe that it will be exciting to meet them.
3.00+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Physics questions
-
For the ground state of the one-dimensional harmonic oscillator, compute the standard deviations x and px and check that the uncertainty principle is obeyed. Use the results of Prob. 4.9 to save time.
-
The interatomic potential for diatomic molecules like O 2 and N 2 can be approximated near its minimum by a simple harmonic oscillator potential 1/2 kx 2 . Consider the classical motion of a diatomic...
-
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...
-
machine element is made of an alloy with Yield strength of 200 Mpa and fracture strain is 0.08. A machine element is characterized by the normal stress components as shown in the figure. The Answer...
-
Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 360 km above the earth's surface, while that for satellite B is at a height of 720 km. Find the...
-
Compute the current yield of an 8%, 10-year bond that is currently priced in the market at $1,100. Use annual compounding to find the promised yield on this bond. Repeat the promised yield...
-
What was the arithmetic average return to PDL during this period? a. 4.32% b. 6.45% c. 6.89% d. 7.78% 2001 2002 Year Return (%) 37.34 -23.67 2003 15.45 2004 17.87 2005 -8.08
-
The Prism gas permeation process developed by the Monsanto Company is highly selective for hydrogen when using hollow-fiber membranes of materials such as silicone-coated polysulphone. In a typical...
-
Follow the steps in Ex. 91.2 to prove the following on your paper. Does the proof work out for f'(x)- g'(x), too? Type yes or no. Correct spelling required. Help: Lecture 91, Ex. 91.2 d 291 Use the...
-
1. Explain the role of cognitive shortcomings in the WorldCom fraud and how social and organizational pressures influenced Betty Vinson's actions. 2. The SEC action against Vinson was deemed...
-
Show that the usual relation E = p 2 /2m arises as the leading momentum dependence of the energy in an expansion of the relativistic p relation? for small p ? mc. Vmc + p?c E 24 C* + pc2
-
The energy required to remove an electron from an atom is called the ionization energy. Predict the energy needed to ionize the last electron from an atom with atomic number Z. (The atomic number is...
-
Factor the given expressions completely. 8a 6 + 64a 3
-
A project your firm is considering requires an investment today of $58,000 and isforecastedto generate cash flows at years 1 through 14 (payments at t = 1 through t = 14) of $15,300 and a cash flow...
-
The Robinson Corporation manufactures automobile parts. During the year, the company sold $5,200,000 of parts that had a cost of $3,500,000. At year end, these are the balances for cost of goods sold...
-
In the article Robo-Advisors Want to Automate Your Retirement. Here's What They're Offering, author outlines the many benefits offered by robos to retirees. Required: List and describe 3 ways in...
-
Can you elucidate the concept of phenotypic plasticity and its role in mediating organismal responses to environmental variation, including the molecular and physiological mechanisms underlying...
-
Why is it important to consider risk and return when building an investment portfolio for a company? Provides examples of how an appropriate balance between risk and return can impact the financial...
-
A proton moves from a location where V = 75 V to a spot where V = -20 V. (a) What is the change in the protons kinetic energy? (b) If we replace the proton with an electron, what is the change in...
-
For the following exercises, find the area of the triangle. Round to the nearest hundredth. 22 50 36
-
In Example 13.5 (Section 13.3) we ignored the gravitational effects of the moon on a spacecraft en route from the earth to the moon. In fact, we must include the gravitational potential energy due to...
-
An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and...
-
Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: A 2.50-kg stone thrown upward from the ground at 12.0 m/s...
-
Surf Ltd has a division which provides civil works contracts to mining companies. As a result of increased costs and lower margins in mining contracts, on July 17 2023, Surf Ltd's directors made the...
-
Chad and Kay are preparing their income tax returns. The couple reports their eligible medical expenses on a calendar year basis. If their eligible medical expenses amount to $2,303.20 and the...
-
The Unit 6 Assignment contains a case study Mt. Hood Furniture and a problem involving PPS sampling. At the completion of the assignment, you should have a practical understanding of the process of...
Study smarter with the SolutionInn App