Question

Consider a system of five particles inside a container where the energy levels are evenly spaced. (For instance, the particles could be trapped in a one-dimensional harmonic oscillator potential.) In this problem, you will consider the allowed states for the system if the particles are identical fermions, identical bosons, or distinguishable particles.

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Consider these systems at a very high temperature. Speculate how the fermionic system, the bosonic system, and the distinguishable particle systems would differ, and support your stance with sound reasoning.

Answer 1

The theory of fermionic systems is an approach to describe fundamental physics.It provides the unification of weak,strong,and the electromagnetic forces with gravity at the level of classical field theory.fermionic system give a rise to a space time together with additional structures that generalize objects like spinors,the metric and curvature.It comprises quantum objects like wave functions and a fermionic fock state.fermionic systems have mathematically sound limiting cases that give a connection to conventional physical structures.so the sound limiting cases are   

• Quantum mechanics and classical field equations
• The Einstein field equations

Boson systems obey bose-einstein statistics which encourages identical bosons to crowd into one quantum state,but not any state is convenient for it.Bosons can interact intermolecular force on a very close approach.It is said that Higgs boson has a role in sound reasoning in boson systems.It is due to these important characteristic that there is no restrictions of bosons that occupy the same quantum state.

Distinguishable particle system consists of particles that can be distinguished.There are two methods for distinguishing between particles.First method relies on differences in the intrinsic physical properties of particles such as mass, electric charge and spin.If there is no difference then it is possible to distinguish between the particles by measuring the relevant properties.The second method is to track the trajectory of each particle.so distinguishable particles can be related with the properties of sound.When we make a difference between these three systems sound has a proper relation with the properties of these systems.