Final answer:
The time-reversed wave function is ψ∗(x,t), which involves taking the complex conjugate of the original wave function, not merely replacing time with its negative.
Step-by-step explanation:
The time-reversed wave function is ψ∗(x,t), not ψ(x,−t).
In quantum mechanics, the time-reversal operation involves complex conjugating of the wave function. When you take the complex conjugate of a wave function Ψ(x,t), you are essentially flipping the sign of the imaginary component, resulting in the time-reversed wave function ψ∗(x,t).
On the other hand, simply replacing time t with −t in the wave function ψ(x,t) does not time-reverse the wave but instead evaluates the original wave at a negative time. The key difference is that time-reversal is not simply running the clock backward but involves dealing with complex numbers, where you take the complex conjugate to achieve the time-reversal effect.