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Although the relative motion and that of the centre of mass cannot in general be separated for an exciton in a quantum well, there is an amusing special case where this is possible. Let Ve and Vh both be parabolic with the same frequency, so
Show that separation into RCM and R is now possible. Unfortunately one still has to solve the equation involving the relative coordinate with both the parabolic potential and the interaction. Sometimes the further approximation is made that the interaction is parabolic in R, rather than 1/R; show that this makes the problem simple.
The results are more useful when applied to an electron (or hole) gas in a parabolic potential, because they show that the motion of the centre of mass is independent of interactions between the electrons. This is known as Kohn theorem and is important in determining the infrared response of doped quantum wells, dots, or superlattices.
What is the emf of a battery with a 0.15ohm internal resistance if the battery delivers 2.0A to an externally connected 5.0ohm resistor
a support cable runs from the top of the boom to the tractor. The angle between the support cable and the horizontal is 32°, and the angle between the boom and the horizontal is 48°.
Suppose unpolarized light of intensity 244 W/m2 falls on the polarizer in the figure, and the angle in the drawing is 36.0°. What is the light intensity reaching the photocell
On a frictionless ice a variable force P in Newtons, expressed by P= 5 + 6 t, is applied to an initially stationary block of wood to move it across the ice until its final speed is V= 25 m/sec. The mass of the wood is M= 3 kg. Vectors P and V are ..
A college student produces about 127 kcal of heat per hour onthe average. What is the rate of energy production in watts? How many kilocalories of heat does the operation of a 1195 Whair dryer produce each second?
A turbine fan in a jet engine has a moment of inertia of 2.5 kgm^2 about its axis of rotation. Find the fan's angular momentum and the net torque acting on the fan as functions of time
A 29-cm-circumference loop of wire has a resistance of 0.17 Ω . The loop is placed between the poles of an electromagnet, and a field of 0.45 T is switched on in a time of 15 ms.
In the circuit, the capacitor is fully charged when switch S is closed. Calculate the time needed for the potential energy stored by the circuit to be equally distributed between the capacitor and inductor. The capacitance is 10.0 mF and inductanc..
The dielectric to be used in a parallel-plate capacitor has a dielectric constant of 2.40 and a dielectric strength of 1.60 107 V/m. What is the minimum area the plates of the capacitor may have
Calculate the change in potential energy of a 92.8 kg man when he takes an elevator from the first floor to 29th floor, if the distance between floors is 4.41 m.
An air plane traveling at 201m/s makes a turn. what is the smallest radius of the circular path (in km) that the pilot can make and keep the centripetal acceleration under 5.0 m/s^2?
A current of constant density, J0, flows through a very long cylindrical conducting shell with inner radius a and outer radius b. What is the magnetic field in the regions rb
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