Average Occupancy of Lower Energy Level in Quantum Mechanics

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The discussion centers on calculating the average occupancy of the lower energy level in a system of N bosons with two energy levels, 0 and E, under Bose-Einstein statistics. At absolute zero temperature, all bosons occupy the lower energy level, while at temperatures above zero, the occupancy depends on the total energy of the system. The relationship between temperature and average energy per boson is emphasized, indicating that additional energy parameters are necessary for a complete answer. The unique properties of bosons, such as not adhering to the Pauli exclusion principle, allow multiple particles to occupy the same energy level. For temperatures above zero, specific formulas from Bose-Einstein statistics are required to determine the average occupancy of the lower energy level.
torchbear
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Hi, can anybody help me with this problem? I am currently study quantum mechanics and am confused with the BE staticstics. OK, say there are N Bosons in a system with two energy levels. The lower energy level is 0 and the upper level is E. The question is what is the average occupancy of the lower energy level? And how about when N goes to infinity?
 
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If the Temperature is zero, then none of the bosons have excess Energy,
so they are ALL in the low Energy Level. If there is a known amount of Energy (or a known average amount per boson) then there must be enough bosons occupying the upper level so that their Energies add up to the total known amount.

In many realistic situations, information about the average Energy per object is given in terms of "Temperature", related via kinetic theory.
 
lightgrav said:
If the Temperature is zero, then none of the bosons have excess Energy,
so they are ALL in the low Energy Level. If there is a known amount of Energy (or a known average amount per boson) then there must be enough bosons occupying the upper level so that their Energies add up to the total known amount.

In many realistic situations, information about the average Energy per object is given in terms of "Temperature", related via kinetic theory.

Thank you for your help. Let me make it clear, the occupancy of any energy level is decided by the total energy of the system, so my question cannot be answered only if we add an additional energy parameter, right?
 
Bosons unlike fermions does not obey pouli exclusion principle. Therefore more than one particle can occupy a single energy level. At T = 0, all the particles condense to the lowest energy level.

For T>0, you may have to use the formulas given by the BE statistics to find the average occupancy of the zero level. See what connection it has to the total number of particles. Following site might be helpful.

http://en.wikipedia.org/wiki/Bose-Einstein_statistics

Gamma.
 
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Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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