Quantum particle of mass m m is bound in the ground state of the one-dimensional parabolic potential well K 0 x 2 2 K0x22 until time t = 0 t=0. Between time moments of t = 0 t=0 and t = T t=T the stiffness of the spring is ramped-up as K ( t ) = K 0 + t T [ K 1 − K 0 ) 0 ≤ t ≤ T ( 3 ) K(t)=K0+tT[K1−K0)0≤t≤T(3) and it stays equal to K 1 K1 afterwards, at t > T t>T. The overall change of the stiffness is small: | K 1 − K 0 | ≪ K 0 |K1−K0|≪K0.

(a) Does any work need to be done to exercise this ramp-up? Can this work be dependent on the duration T of the ramp-up and why?

(b) If the answer to the latter question is positive, evaluate the needed work in the lowestorder of the perturbation theory.

(c) Analyze the T-dependent part of the work, if any, and find out how much of the variation in the amount of work is achieved between the adiabatic ( T → [infinity] T→[infinity]) and nearly instantaneous ( T → 0 T→0)limits?

How do the measurements of charge at the different locations on the sphere compare to each other? the charge measurements are different at all locations on the sphere. the charge measurements are virtually not the same at all locations on the sphere except for the charge at the very top and at the very bottom that are equal. the charge measurements are virtually the same at all locations on the sphere except for the charge at the very top. at the top, the conductive sphere has a small disk that is made of different material. the charge measurements are the same at all locations on the sphere. what happens to the charge on the conductive sphere when it is connected to a source of charge such as the electrostatic voltage source? nothing will happen because no charge goes around the surface of the sphere. the charge on the conductive sphere spreads out over the surface of the sphere; being greater in some specific locations on the sphere. the charge on the conductive sphere spreads out uniformly over the surface of the sphere. the charge on the conductive sphere spreads out non-uniformly over the surface of the sphere.

What do elements in a family tend to share. a.) similar periods b.) similar groups c.) similar atomic symbols d.) similar chemical properties and characteristics

Which statement is best supported by the information in the chart? wave y is moving the fastest. wave x is moving the fastest. all of the waves are moving at the same speed. all of the waves have the same value of wavelengths per second.