Final answer:
There is a total of four distinct states for the three-boson system.
For a system of three indistinguishable bosons that can each be in one of two states, there are four distinct states. These states arise from the different possible distributions of the bosons among the two states since bosons are not subject to the Pauli exclusion principle and can occupy the same state.
Step-by-step explanation:
The question asks about the number of distinct states for a three-boson system, where each boson can be in one of two states. In quantum mechanics, bosons are particles that adhere to Bose-Einstein statistics, which allows multiple identical particles to occupy the same quantum state. Therefore, unlike fermions which must obey the Pauli exclusion principle, bosons do not have this restriction.
To calculate the number of distinct states for the three-boson system, we can employ a combinatorial method. As bosons are indistinguishable and can occupy the same state, we should consider the different ways in which three bosons can be distributed among the two states.
Let's denote the two states as state 1 and state 2. The possible distributions are:
- All three bosons in state 1: (3,0)
- Two bosons in state 1 and one in state 2: (2,1)
- One boson in state 1 and two in state 2: (1,2)
- All three bosons in state 2: (0,3)
Since each configuration is distinct and the particles are indistinguishable, we have a total of four distinct states for the three-boson system.