Answer to Question #166027 in Quantum Mechanics for khalida

Question #166027

Find the wave function of two systems of identical, noninteracting particles: first consists of two bosons

and the second of two spin-1/2 fermions.


1
Expert's answer
2021-02-25T17:52:55-0500

Consider two identical, non interacting particles (1 and 2) which may exist in two different states a and b.


ΨI=Ψa(1)Ψb(2)\Psi_I = \Psi_a(1) \Psi_b(2)


ΨII=Ψa(2)Ψb(1)\Psi_{II} = \Psi_a(2) \Psi_b(1)


If the particles are indistinguishable, then we cannot tell whether the number is in state Ψ1\Psi_1 or Ψ2\Psi_2 and because both states are equally likely we write the system wave function as a linear combination of Ψ1andΨ2\Psi_1 and \Psi_2 .


If the particles are bosons, the system wave function is symmetric :


Ψb=12[Ψa(1)Ψb(2)+Ψ(2)Ψ(1)]=Ψs\Psi_b = \dfrac{1}{\sqrt2}[\Psi_a(1)\Psi_b(2)+\Psi(2)\Psi(1)] = \Psi_s


If the partices are fermions, the wave function is antisymmetric


ΨF=12[Ψa(1)Ψb(2)Ψa(2)Ψb(1)]=ΨA\Psi_F = \dfrac{1}{\sqrt2}[\Psi_a(1)\Psi_b(2)-\Psi_a(2)\Psi_b(1)] = \Psi_A


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS