Identical particles, spin, fermions, etc.

In summary, the task is to compute the energy and wavefunctions for the three lowest states of two spin-(1/2) particles in a finite length box, with the particles in a singlet spin state. The equations used are E = \epsilon_{1} + \epsilon_{2} +... and the wavefunctions are assumed to be a product of a symmetric spatial part and an antisymmetric spin part due to the singlet state. There is also a question regarding the ground and excited states and the assumption that the particles are fermions.
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Void123
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Homework Statement



I got two particles, spin-(1/2), in a box of finite length and I must compute the energy and wavefunctions for the three lowest states. The particles are in a singlet spin state.



Homework Equations



[tex]E = \epsilon_{1} + \epsilon_{2} +...[/tex]



The Attempt at a Solution



I got the wavefunctions down.

Just want to clarify some uncertainty here, if the ground state is just going to be for n = 1, 2, then would the first excited state be n = 1, 3, and second excited state n = 2, 3?

I am also assuming they're fermions.
 
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Also, I have assumed that since the total spin is in the singlet state, therefore the wavefunction will be the product of the symmetric spatial part and the antisymmetric spin part. Is this correct?
 

FAQ: Identical particles, spin, fermions, etc.

What are identical particles and how are they different from non-identical particles?

Identical particles are particles that cannot be distinguished from one another based on their physical properties. This means that they have the same mass, charge, and other characteristics. Non-identical particles, on the other hand, can be distinguished from one another based on their individual properties.

What is spin and why is it important for identical particles?

Spin is an intrinsic property of particles that describes their angular momentum. Identical particles have the same spin, which can be either integer or half-integer values. This is important because particles with half-integer spin are classified as fermions, while particles with integer spin are classified as bosons. These classifications have important implications for the behavior and interactions of identical particles.

3. How do identical particles interact with each other?

Identical particles can interact with each other through fundamental forces, such as electromagnetism and the strong and weak nuclear forces. However, due to the Pauli exclusion principle, identical fermions cannot occupy the same quantum state, meaning they cannot be in the same place at the same time. This leads to unique behaviors and properties for identical particles, such as the formation of atoms and molecules.

4. What are fermions and why are they important in particle physics?

Fermions are particles that have half-integer spin, such as electrons, protons, and neutrons. They follow the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state. This principle is crucial in understanding the structure of matter and determining the stability of atoms and molecules.

5. How do identical particles contribute to the concept of entanglement?

Entanglement is a phenomenon in quantum mechanics where two or more particles become connected in such a way that the state of one particle is dependent on the state of the other particles, even when they are separated by large distances. Identical particles can become entangled through their interactions, leading to interesting quantum effects and potential applications in quantum computing and communication.

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