Average Occupancy of Lower Energy Level in Quantum Mechanics

In summary, the average occupancy of the lower energy level is determined by the total energy of the system, but if the temperature is zero, then all of the bosons have excess energy and are 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.
  • #1
torchbear
6
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 

What is the average occupancy of lower energy level in quantum mechanics?

The average occupancy of lower energy level in quantum mechanics refers to the average number of particles or systems that occupy the lowest possible energy level in a given quantum system. It is a measure of the number of particles that are in the ground state of the system.

How is the average occupancy of lower energy level calculated in quantum mechanics?

The average occupancy of lower energy level is calculated by taking the sum of the probabilities of each possible energy state being occupied by a particle, multiplied by the number of particles in that state. This sum is then divided by the total number of particles in the system.

Why is the average occupancy of lower energy level important in quantum mechanics?

The average occupancy of lower energy level is important because it provides valuable information about the behavior and properties of a quantum system. It can help us understand the stability and dynamics of the system, as well as its response to external stimuli.

How does the average occupancy of lower energy level change with temperature in quantum mechanics?

In quantum mechanics, as temperature increases, the average occupancy of lower energy level tends to decrease. This is because particles gain more thermal energy and are more likely to occupy higher energy levels, leaving fewer particles in the ground state. This relationship is described by the Boltzmann distribution.

Can the average occupancy of lower energy level be greater than 1 in quantum mechanics?

No, the average occupancy of lower energy level cannot be greater than 1 in quantum mechanics. This is because the average occupancy is a probability and probabilities cannot exceed 1. A probability of 1 means that the event (i.e. occupying the lowest energy level) is certain to occur.

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