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- During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to estimate the wavespeed of an atomic bomb explosion. He assumed that theblast wave radius R was a function of energy released E , airdensity ρ , and time t . Use dimensional reasoning to showhow wave radius must vary with time.The sin and cos version can be derived thru Schrodinger (in terms of particle in a box) in complex exponential form. Show that C and D are constants that can be expressed in terms of A and B using Euler's formula.write down the average of a plank oscillator and show the that its leads to the classical result under the condition of high temperature. (b) what is the average energy of one dimesnional classical oscillator?
- Con der the SysZem ( Cycle id) descsibed by x= a(l+sino) Y = all-caso) find ) the Kinefic eneryy of Hhe Systeam 4) ーTZ02T %3D Lagrangían (iji) the ca nonical momentum and the total energiy of the syafeyy and its eguetien of metion-Calculate the value of the characteristic times for the tiny oildrop in the milliken experiment when its terminal speed is 6.1×10^-5 m/sFollowing problem;
- (a) Assıning that nonrelativistic quantum mechanics is invariant un- der time reversal, derive the time reversed form of the Schrödinger wave functiou. (h) What is the quantumi nechanical Hamiltonian for a free electron with magnetic inoment µ in the external constant magnetic ficld H, in the z-clircction, in the reference frame of the clectron? (c:) Suppose that an extra constant inaguetic ficled Hy is imposed in the y-clirection. Determine the forn of the quantum mechanical operator for the time rate of change of u iu this case.For a system of particles at room temperature (300K), what value must & be before the Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann distributions agree within 0.1% ? Justify your answer.A positively charged particle moving to the right is stoppedrapidly. Sketch the resultant radiated pulse.
- Sketch the expected occupation number for a state with energy ε as a function of the temperature T when the particles are (i) bosons or (ii) fermions, and explain how these simplify when the system is dilute.An electron trap in an intinite potentiad Well Electron can be considered a S free particle - having partick and energy UIS (*) sing - * २), 77 7. 7U 2. I th the pind probabilit of Kinetic 77x> write down the schrodinger eguation for the electron in infante potential wellThe probabi tiy particle is in the nd stete Cn-1) that the gro The probobulity thal the partick is in tha fist excted stae Cn=2) 1 The stalo nJwith the highest probability of having the pardicle