For this problem, ignore spontaneous emission. Consider a particle of mass m, and charge q in...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
For this problem, ignore spontaneous emission. Consider a particle of mass m, and charge q in a 1-dimensional box of length L. The unperturbed Hamiltonian Ho is just Hamiltonian of this system. We drive it with one or more electric field pulses. Each pulse is described by: H'=- =-Eoqzf(t) Where [cos (wt), 0<t<r otherwise, f(t)= We can assume that r>. We start with the system in the ground state 1). 1. What are the first 3 energies of the unperturbed system? 2. We wish to design a pulse which puts the system in the state (11)+(2)). What frequency w and time ry should we use? 3. We now wish to add a second pulse which takes the system from the state (1) + 2)) and puts it in (11)+13)). What frequency and time 72 should we use for this pulse? 4. Does the final state (11)+13)) radiate? If so, at what frequency? 5. You could design a third pulse, with duration and time 73, which would take the system from (1) + 3)) to (11) + 4)). Would this final state radiate? If so, at what frequency? Express the frequency as a simple function of w₁, 2, and w E, as a function of time frequency Amplitude E frequency ₂ UNE For this problem, ignore spontaneous emission. Consider a particle of mass m, and charge q in a 1-dimensional box of length L. The unperturbed Hamiltonian Ho is just Hamiltonian of this system. We drive it with one or more electric field pulses. Each pulse is described by: H'=- =-Eoqzf(t) Where [cos (wt), 0<t<r otherwise, f(t)= We can assume that r>. We start with the system in the ground state 1). 1. What are the first 3 energies of the unperturbed system? 2. We wish to design a pulse which puts the system in the state (11)+(2)). What frequency w and time ry should we use? 3. We now wish to add a second pulse which takes the system from the state (1) + 2)) and puts it in (11)+13)). What frequency and time 72 should we use for this pulse? 4. Does the final state (11)+13)) radiate? If so, at what frequency? 5. You could design a third pulse, with duration and time 73, which would take the system from (1) + 3)) to (11) + 4)). Would this final state radiate? If so, at what frequency? Express the frequency as a simple function of w₁, 2, and w E, as a function of time frequency Amplitude E frequency ₂ UNE
Expert Answer:
Answer rating: 100% (QA)
1 The first 3 energies of the unperturbed system are given by E1 h2mL E2 h32mL and E3 h52mL where h ... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
A particle of mass m and charge q moves at high speed along the x axis. It is initially near x = -7, and it ends up near x = 7. A second charge Q is fixed at the point x = 0, y = -d. As the moving...
-
For a particle of mass m and charge q moving in a circular path in a magnetic field B, (a) Show that its kinetic energy is proportional to r2, the square of the radius of curvature of its path. (b)...
-
Consider a particle of mass m whose motion starts from rest in a constant gravitation field. If a resisting force proportional to the square of the velocity (i.e., kmv2) is encountered, show that the...
-
What is the equal payment series for 12 years that is equivalent to a payment series of $25,000 at the end of the first year, decreasing by $1,200 each year over 12 years? Interest is 7% compounded...
-
After you restore files following an incident, users complain that some of their data files are missing. What might have happened?
-
A sign of weight W is supported at its base by four bolts anchored in a concrete footing. Wind pressure p acts normal to the surface of the sign; the resultant of the uniform wind pressure is force F...
-
For each of the following, (a) calculate the mean, standard deviation, and standard error of the mean for each Group and (b) construct a bar graph (assume the independent variable is condition and...
-
A wholesale distributor operating in different regions of Portugal has information on the annual spending of several items in their stores across different regions and channels. The data (Wholesale...
-
Following are the transactions of a new company called Pose-for-Pics. August 1 M. Harris, the owner, invested $10,500 cash and $45,150 of photography equipment in the company in exchange for common...
-
Profits have been decreasing for several years at Pegasus Airlines. In an effort to improve the company?s performance, consideration is being given to dropping several flights that appear to be...
-
What is the definition of an OSPF link? Two routers participating in OSPF routing Two routers that share the same area ID Routed interface added to the OSPF process Two routers that share the same AS...
-
c) A wooden beam (Specific gravity = 0.64) is 140 mm by 5 m and is hinged at A, as shown in Fig 3.2. At what angle, the beam will float in water? 5m +(5-L) 0 Fig 3.2 Water VW beam t (40%)
-
The system shown consists of 3 cables. For example; cable C12 joins points 1 and 2. The coordinates of point 1 are (6.4, 0, 0) m, those of point 2 are (0, 9.5, -6.1) m, and those of point 3 are (0,...
-
Figure Q1 shows a beam with pivots at A and D. There are three loads located at positions B, C and E (as illustrated). The leftmost load is 8 kN located at position B. The rightmost load is 16 kN...
-
. An aircraft wing may be represented by a single horseshoe vortex of span 20 and circulation strength 25ms1. Calculate the downwash angle of a point 15 downstream of the bound vortex, in the plane...
-
How many kilograms of water must evaporate from a 49.2 kg woman to lower her body temperature by 0.708C? The latent heat of vaporization for water at 37C is 580 kcal/kg and the specific heat of the...
-
== This state diagram defines an NFA M ({90, 91, 92), 6, 40, {q0, q1}) accepting some language L over the alphabet = {0, 1}. Step by step follow the algorithm to trans- form this NFA into an...
-
Express these numbers in standard notation. a. 2.87 10-8 b. 1.78 1011 c. 1.381 10-23
-
Shown in Fig. 4.31 are the front and rear wings of an Indy racing car. These wings generate down force, which is the vertical downward force produced by the air moving over the car. Why is such a...
-
A yoyo with an axle diameter of 1.00 cm has a 90.0cm length of string wrapped around it many times in such a way that the string completely covers the surface of its axle, but there are no double...
-
A student weighing 800 N crouches on a scale and suddenly springs vertically upward. His roommate notices that the scale reads 900 N momentarily just as he leaves the scale. With what acceleration...
-
Given the four criteria necessary for a sale to be complete, which of the following is not one of those conditions? 1. Delivery has occurred or services rendered. 2. Cash has been collected. 3. The...
-
What is the difference between a business and a pure charity? Between a business and a governmental agency?
-
Sketch the \(P-V\) phase diagram for helium-4 using the sketch of the \(P-T\) phase diagram in Figure 4.3. Ps P S superfluid Pe T To T FIGURE 4.3 Sketch of the P-T phase diagram for helium-4. The...
Study smarter with the SolutionInn App