Question

Consider two non-interacting particles confined to a one-dimensional box with infinite potential barriers. Their wavefunctions are \( \psi_1 \) and \( \psi_2 \), and energies are \( E_1 \) and \( E_2 \), respectively. The INCORRECT statement(s) about this system is/are:

• A. The total energy is \( E_1 + E_2 \)
• B. The total wavefunction is \( \psi_1 + \psi_2 \)
• C. The total energy is \( E_1 E_2 \)
• D. The total wavefunction is \( \psi_1 \psi_2 \)

Hint:

In quantum mechanics, for non-interacting particles, the total wavefunction is the product of the individual wavefunctions, and total energy is the sum of individual energies.

Answer 1

The Correct Option is B, C

For two non-interacting particles in a 1D box:

• The total energy of the system is the sum of individual energies:
  \( E_{\text{total}} = E_1 + E_2 \)   CORRECT
• The total wavefunction is the product of individual wavefunctions:
  \( \Psi_{\text{total}} = \psi_1 \psi_2 \)   CORRECT
• A sum of wavefunctions \( \psi_1 + \psi_2 \) does not represent the correct combined state.   WRONG
• Product of energies \( E_1 E_2 \) is not physically meaningful in this context.   WRONG

\[ \boxed{\text{Incorrect statements: (B) and (C)}} \]