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A Fermi gas of only two particles, assume that each particle can be in one of three possible quanta states, s = 1, 2, 3. The possible number of states of the whole gas is?
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Possible Number of States in a Fermi Gas of Two Particles
Introduction
In a Fermi gas, each particle obeys the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. The total number of possible states for a system of two particles can be determined by considering the number of possible combinations for each particle.
Number of States for Each Particle
Since each particle can be in one of three possible quanta states (s = 1, 2, 3), the number of states for each particle is 3.
Combinations of States for Two Particles
To determine the number of possible combinations of states for the whole gas, we need to consider the possible combinations of states for the two particles.
Since the particles are indistinguishable, we cannot simply multiply the number of states for each particle. Instead, we need to consider all possible combinations while avoiding double counting.
Combination 1: Particle 1 in State s1 and Particle 2 in State s2
In this combination, there are 3 possibilities for Particle 1 (s1 = 1, 2, 3) and 2 possibilities for Particle 2 (s2 = 1, 2, 3 excluding the state occupied by Particle 1). Therefore, there are 3 x 2 = 6 possible combinations for this case.
Combination 2: Particle 1 in State s2 and Particle 2 in State s1
Since the particles are indistinguishable, this combination is equivalent to Combination 1. Therefore, there are also 6 possible combinations for this case.
Combination 3: Particle 1 in State s1 and Particle 2 in State s3
In this combination, there are 3 possibilities for Particle 1 (s1 = 1, 2, 3) and 2 possibilities for Particle 2 (s3 = 1, 2, 3 excluding the state occupied by Particle 1). Therefore, there are 3 x 2 = 6 possible combinations for this case.
Combination 4: Particle 1 in State s3 and Particle 2 in State s1
Since the particles are indistinguishable, this combination is equivalent to Combination 3. Therefore, there are also 6 possible combinations for this case.
Combination 5: Particle 1 in State s2 and Particle 2 in State s3
In this combination, there are 3 possibilities for Particle 1 (s2 = 1, 2, 3) and 2 possibilities for Particle 2 (s3 = 1, 2, 3 excluding the state occupied by Particle 1). Therefore, there are 3 x 2 = 6 possible combinations for this case.
Combination 6: Particle 1 in State s3 and Particle 2 in State s2
Since the particles are indistinguishable, this combination is equivalent to Combination 5. Therefore, there are also 6 possible combinations for this case.
Total Number of Possible States
To calculate the total
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A Fermi gas of only two particles, assume that each particle can be in one of three possible quanta states, s = 1, 2, 3. The possible number of states of the whole gas is?
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A Fermi gas of only two particles, assume that each particle can be in one of three possible quanta states, s = 1, 2, 3. The possible number of states of the whole gas is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A Fermi gas of only two particles, assume that each particle can be in one of three possible quanta states, s = 1, 2, 3. The possible number of states of the whole gas is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Fermi gas of only two particles, assume that each particle can be in one of three possible quanta states, s = 1, 2, 3. The possible number of states of the whole gas is?.
A Fermi gas of only two particles, assume that each particle can be in one of three possible quanta states, s = 1, 2, 3. The possible number of states of the whole gas is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A Fermi gas of only two particles, assume that each particle can be in one of three possible quanta states, s = 1, 2, 3. The possible number of states of the whole gas is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Fermi gas of only two particles, assume that each particle can be in one of three possible quanta states, s = 1, 2, 3. The possible number of states of the whole gas is?.
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