Find The energy level, degenercy and first excited state of two identical particles moving in a one-dimensional harmonic oscillator. However, express the eigenstate of a particle as (A) In case of boson (B) In case of fermion In >
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- Let us a8sume that function (at t=0) panticle. in an infinite well ig describet by the following wove 4 (3y0) = J y (x) +능 42(2) + J'g 4'3 (x) Then if we a meagurement of energy ig made then find out the energies and probabilitieg corregpontine to them. How wl wave function evolve with time ie w(x,) ? What uill be the average energy T Carry outCon 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-(b) Suppose a particle trapped in an one-dimensional box of width a with infinitely hard walls. Derive the normalized wave function from the solution of wave function? Find the probability of particle that can be found between 0.4a and 0.5a for the first excited state.
- Problem 5.3 The partition function of a system is given by log Z = al*V where a is a constant, T is the absolute temperature and V is the volume. Calculate the internal energy, the pressure and the entropy.. (1) Find the kinetic, potential and total energies of the hydrogen atorn in the 2nd excited level.A particle in an infinite potential box with walls at 0 and xma (ie, the potential is infinite fort 0 and Su and zere in berween) has the following wave function at some initial time: 3x (x)= sin (a) Find the possible results of the measurement of the system's energy and the correspond- ing probubilities. ib) Find the form of the wave function afier such a measurement. (c) If'the energy is measured again ummediately afterwards, what are the relative probabili- ties of the possible outcomes?
- 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.Suppose you have three particles, and three distinct one-particle states (Va(x), Vb(x), and ye(x)) are available. How many different three-particle states can be constructed, (a) if they are distinguishable particles, (b) if they are identical bosons, (c) if they are identical fermions? (The particles need not be in different states-Wa(x1)¥a(x2)ựa (.x3) would be one possibility, if the particles are distinguishable.) |