السلام عليكم ورحمة الله وبركاته
أسال الله التوفيق للجميع
انا طالب في الفيزياء مرحلة الماستر وهذا اول ترم لي وعندي
واجب من قبل امس وانا ابي اوصل للحل وما وصلت
احتاد منكم المساعده تكفووووووووووووووووووون
ودمتم
. /10/ Consider a system of two neutrons interacting only through gravita-
tional attractive forces. Find the binding energy of this quantum \atom"
(in eV) and the characteristic size of the ground state con guration. Is
there any chance to nd such a system in reality?
2. /12/ Consider a particle of mass m in the uniform gravitational eld of
the Earth (the Earth surface is treated as an impenetrable plane).
a. Using the semiclassical quantization, estimate energy and typical height
above the Earth for the ground state of the particle.
b. Give a numerical estimate for the neutron.
c. For the electron one needs to consider in addition the electrostatic
e ects. Assume that the Earth is a perfect conductor and decide what
would be the average height above the Earth of the electron in the ground
state.
3. /10/ a. Starting from the Maxwell distribution for the speed of molecules
in a classical gas, nd the distribution function of the de Broglie wave-
lengths and the most probable de Broglie wave length of hydrogen molecules
at room temperature.
b. Many researchers in various laboratories study the Bose-Einstein con-
densation of identical atoms in atomic traps. This phenomenon starts
when, as temperature decreases, the de Broglie wavelength of thermal
motion of the atoms grows up to the average distance between atoms.
Estimate the necessary density of atoms with the mass number A = 100
in the trap, if the condensation temperature is T = 107K.
4. /8/ A particle of mass m is moving in one-dimensional harmonic oscillator
potential U(x) = (1=2)kx2. We know that the energy spectrum is discrete
and equidistant,
En = h!
n +
1
2
; n = 0; 1; 2; :::; ! =
r
k
m
: (1)
How will this spectrum change if the particle carries an electric charge e
and an external electrostatic eld E is applied along the x-axis