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Griffiths Quantum Mechanics - Identical Particles (Wavefunctions)

An example in Griffith's Intro. to Quantum Mechanics is: Suppose we have two non-interacting particles both of mass $m$ in a infinite square well. The one particle states are $$\phi_n (x) = \sqrt{\...
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0answers
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Spectrum of two particles system hamiltonian

Consider the following hamiltonian describing a system of two identical spin 1/2 particles in one dimension: $$H = H_1 +H_2 - \lambda \vec {s_1} . \vec {s_2}$$ Where $H_i$ is the Hamiltonian of an ...
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3answers
248 views

Decay of neutral kaon into two pions and conservation of angular momentum

I am asked the following question: A kaon $K^0$ decays into two pions $\pi^0$, being this two pions particles with spin zero. Using the conservation of angular momentum and the fact that the two pions ...
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1answer
103 views

Does entropy really not increase here?

Two vessels separated by a partition have equal volume $V_0$ and equal temperature $T_0$. They both contain the same ideal gas, and the particles are indistinguishable. The left vessel has pressure $...
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1answer
472 views

Finding states of a system of 2 identical bosons (including spin)

I'm trying to find the ground state and first excited state for 2 identical bosons in an infinite square well. I know that both states are degenerate and the spatial and spin parts of the wave ...
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1answer
201 views

Understanding concepts of $N$ identical particles

I'm uncomfortable with the concepts of $N$ number of identical fermions and identical bosons and their degeneracies and energies. For example, lets say we a have a 3-dimensional isotropic harmonic ...
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2answers
720 views

Pauli matrix for triplet state?

Question is, what would be the result of applying the operator $\hat A = [3I + \vec\sigma_1 . \vec\sigma_2]$ on the |singlet$\rangle$ and |triplet$\rangle$ states ($\vec\sigma_1$ acts on the 1st ...
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1answer
211 views

Quantum: How do I find the degeneracy of 2 electrons in an infinite cube (3D) well? [closed]

There are two electrons inside an infinite potential cube well (essentially $V=\infty$ outside a cube and $0$ inside it) and I need to find the degeneracy of the first excited state. I'm thinking it ...
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0answers
3k views

Three particles case, finding ground energy state

Here I came up with three particles in a box problem. (Assumption: Here I do not consider the interaction between particles and spin for simplicity.) What I want to do is express the ground state's ...
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1answer
89 views

About bosonic, fermionic state in identical particles

The upper picture is my ideas which represent states by using the tensor product. but the lower picture, as you see, includes uppermost states. i don't know how to treat the uppermost states in lower ...
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1answer
78 views

Problem with indistinguishability in partition function

Consider an ideal gas of classical particles of mass $m$ in uniform potential $\xi$ in 3d. The gas $N$ molecules, volume $V$ and is at temperature $T$. I believe that the Hamiltonian of this system is ...
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3answers
658 views

How to determine whether an eigenstate of total spin is symmetric or antisymmetric?

Here we have two identical paticles with spin $I$, integer or half-integer, and there are $(2I+1)^2$ states. Each one of them can be uniquely determined by total spin and its orientation, we can use $...
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2answers
828 views

Indistinguishable particles and probability density

I am given the following (probably simple) exercise, but I think I misunderstand something: Let $\psi_{a,b}(r_1,r_2)$ be a two-particle state, calculate the probability density for distinguishable ...
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1answer
8k views

Ground State Wavefunction of Two Particles in a Harmonic Oscillator Potential

Question: Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by $$H=\frac{p_{1x}^2}{...
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4answers
879 views

Distinguishable, indistinguishable paramagnetic ideal gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...