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derive the formula for the energy density of radiation inside an enclosed cavity
at constant temperature T using classical physics.Show how the classical theory is modified to correctly explain the energy density.
derive the formula for the energy density of radiation inside an enclosed cavity at constant temperature T using classical physics, show how the classical theory is modified.
How long do quantum fluctuations last for?
Like can they in theory, if a long enough period of time passed isnt it possible for, idk, a baseball to suddenly appear. I just want to know. If in theory quantum fluctuations can create matter from nothing and the matter staying in exsistance. Sorry if this question was worded a bit weird.
Calculate phase shifts for quantum scattering, and then in terms of these phases give an ac-
count on scattering amplitude. As an application consider a sphere of radius r, assuming a certain

potential V such that it is infinite inside the sphere and minimum outside the sphere. Calculate phase
shifts for this sphere.
A particle of mass M, initially at rest decays into two particles with rest masses m1 and m2 respectively. Show that the total energy of the mass m1 is

E1= c^(2) [M^(2)+ m1^(2) - m2^(2)] / 2M

c= speed of light
Discuss some applications of Legendre polynomial in physics. Derive in detail
Spherical harmonics Laguerre polynomials

. In Dirac’s theory, the probability current density is defined by the relation j(r, t) = CΨ* αΨ ,

where Ψ is the four component wave vector. Write the relations for jx, jy, jz in terms of the

component of Ψ i.e.

J(r, t) = Ψ*α Ψ ; jx = C Ψ* αx Ψ


Discuss some applications of Legendre polynomial in physics. Derive in detail
Spherical harmonics Laguerre polynomials.
using the equipartition of energy concept estimate the ideal gas Cp(not Cv) in units KB for the low temperature regime where no vibrational modes are activated(if you calculate Cp=42KB, enter 42 as your answer )
Show that
i. σ’x2 = σ’y2 = σ’z(2) = 1
ii. [σ’x , αx ] = 0 ,
[σ’x , αy ] = 2i αz &
[σ’x , αz] = -2i αy
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