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captainjack2000
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Wavefunctions for Indistinguishable and Distinguishable particles - URGENT
A one-dimensional potential well has a set of single-particle energy eigenstates Un(x) with energies En=E_o n^2 where n=1,2,3... Two particles are placed in the well with three possible sets of properties.
a)2 distinguishable spin 0 particles
b)2 identical spin 0 particles
c)2 identical spin 1/2 particles
Write down the spatial part of the two-particle wave functions at t=0 for the two lowest energy states of the two-particle system, and hence give the degeneracies of these energy states and explain how these two-particle wavefunctions depend on time
I am getting incredibly confused by two-particle wavefunctions and between the spatial and spin states...
a) If there are 2 indenticle spin 0 particles: The wavefunction must be symmetric then would the wavefunction just be
(|0>|1> + |1>|0>)/sqrt(2)
b) 2 identicle spin 1/2 particles: The wavefunction must be antisymmetric due to Pauli Exclusion Principle so
(|0>|1> - |1> |0>)/sqrt(2)
c) 2 indistinguishable particles (boson or fermion) would it just be a wavefunction with 6 dimensions
ie phi(r1,r2)
How would you then write the spin part of the wavefunction...and how do they depend on time...
Realise this might be all wrong but I have an exam coming up and would REALLY appreciate someone clarifying this!
Homework Statement
A one-dimensional potential well has a set of single-particle energy eigenstates Un(x) with energies En=E_o n^2 where n=1,2,3... Two particles are placed in the well with three possible sets of properties.
a)2 distinguishable spin 0 particles
b)2 identical spin 0 particles
c)2 identical spin 1/2 particles
Write down the spatial part of the two-particle wave functions at t=0 for the two lowest energy states of the two-particle system, and hence give the degeneracies of these energy states and explain how these two-particle wavefunctions depend on time
Homework Equations
The Attempt at a Solution
I am getting incredibly confused by two-particle wavefunctions and between the spatial and spin states...
a) If there are 2 indenticle spin 0 particles: The wavefunction must be symmetric then would the wavefunction just be
(|0>|1> + |1>|0>)/sqrt(2)
b) 2 identicle spin 1/2 particles: The wavefunction must be antisymmetric due to Pauli Exclusion Principle so
(|0>|1> - |1> |0>)/sqrt(2)
c) 2 indistinguishable particles (boson or fermion) would it just be a wavefunction with 6 dimensions
ie phi(r1,r2)
How would you then write the spin part of the wavefunction...and how do they depend on time...
Realise this might be all wrong but I have an exam coming up and would REALLY appreciate someone clarifying this!