Let where ? ? and ? ? ? are the annihilation and creation operators of two independent

Question:

Let where ? _? and ?^?_? are the annihilation and creation operators of two independent simple harmonic oscillator satisfying the usual simple harmonic oscillator commutation relations. Prove

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Modern Quantum Mechanics

ISBN: 978-0201539295

Revised Edition

Authors: J.J Sakurai

See More Books

Question Posted: Apr 16, 2011 06:41 AM

See More Questions

The frequency of a simple harmonic oscillator is doubled from 0.25 Hz to 0.50 Hz. What is the change in its period?
The ground-state energy of a harmonic oscillator is 5.60eV. If the oscillator undergoes a transition from its n = 3 to n = 2 level by emitting a photon, what is the wavelength of the photon?
Prove that the two relations for entropy change of ideal gases under the constant-specific-heat assumption (Eqs. 733 and 734) are equivalent.
John Hasty opened his bakery on March 1, 1999. The following transactions took place in early March: 1. Deposited $10,000 into a checking account in the name of the Hasty Bakery. 2. Leased a small...
The phase angle in a certain RL circuit is 68 at a frequency of 60.0 Hz. If R = 2.1 for this circuit, what is the value of the inductance, L?
Based on the ER model shown in Figure P11.7 and on the query shown after the figure. Figure P11.7: Should you create an index? Why or why not? INVOICE CUSTOMER LINE PK Cus CODE PK INV_NUMBER PK,FK1...
What do we look for in a normal probability plot to indicate nonnormality? Use the stock price data for Exercises 2426.
Within the food service industry (restaurants that serve meals to customers, but not just fast food), find examples of firms that have sustained competitive advantage by competing on the basis of (1)...
Compute the current ratio and acid - test ratio.Answer is not complete. Complete this question by entering your answers in the tabs below. Compute the days' sales uncollected.
The Buse Sound, Ltd. has three divisions for selling music: Cassette, Vinyl, and CD. The divisions have the following revenues and expenses for June 2022: Cassette Vinyl CD Revenues $82,000 $430,000...
Show for the one-dimensional simple harmonic oscillator where x is the position operator. (Ole**0) = exp[- kc0]x?0)/2], %3D ik.
Consider a particle of mass in subject to a one-dimensional potential of the following form: a. What is the ground-state energy? b. What is the expectation value (x2) for the ground state? for x >0 V...
Do U.S. GAAP and IFRS differ in the criteria they use to determine whether a transfer of receivables is treated as a sale? Explain.
The balances of selected accounts of Casper Company on February 28, 20X1, were as follows: Sales $250,000 and Sales Returns and Allowances $4,000. The firm's net sales are subject to an 7 percent...
1. Draw and label force diagrams for the physics book and for the calculator. Add equality marks showing any equalities between force diagrams. Circle and label any Newton's third law pairs. (6 pts)...
Consider the Lincoln Tunnel, which was built in 1939 under the Hudson River in New York. Assume the tunnel to be empty with perfectly conducting walls and rectangular cross section with width 6.55 m...
Examine a well-known principal-agent contract, the sale of your home by a licensed realtor. You will use the following data to analyze this case. Your home is the typical home, approximately 1,875 sq...
i) Generate a third degree polynomial in x and y named g(x, y) that is based on your mobile number (Note: In case there is a 0 in one of the digits replace it by 3). Suppose your mobile number is...
People understand each others jobs and often do different tasks. 1 2 3 4 5 LO.1
Periwinkle Company is a multinational organization. Its Parts Division is located in Lavender Land, while its Assembly Division is located in North Orchid. During the current year Periwinkle Companys...
Explain the principle behind the finite difference method.
Light of wavelength 340 nm is incident on a metal surface and ejects electrons that have a maximum speed of 3.5 x 105 m/s. (a) What is the work function of the metal? (b) What is its stopping...
A 10.0-keV X-ray photon is successively scattered by two free electrons initially at rest. In the first case, it is scattered through an angle of 41o; the second scattering is through an angle of...
Under the right circumstances, if a photons energy is above a minimum energy level, that energy can be completely converted into creating an electronpositron pair (a positron is identical to an...
All else constant, if the yield to maturity of a bond increases, the the value of the bond __________. a. increases b. decreases c. remains the same d. not enough information To answer enter a, b, c,...
Martha s Vineyard Marine Supply is a wholesaler for a large variety of boating and fishing equipment. The company s controller, Mathew Knight, has recently completed a cost study of the firm s...
1. Compute the productivity profiles for each year. If required, round your answers to two decimal places. 2a. Did productivity improve? 2b. Explain why or why not

Let where ? ? and ? ? ? are the annihilation and creation operators of two independent

Question:

J. = (at a, - at a ), J = ha' a z. N = a, a, + a a. %3! %3! h2 J? = 2 [J', J.] = 0, :-)MG)-} [J., J,]= hJ +1

Step by Step Answer:

We know that aa 1 and aa aa 0 since oscillators are inde pendent then JJ aaaa aaa...View the full answer

Modern Quantum Mechanics

Students also viewed these Modern Physics questions