The expression |y(x, t)|2 stands for(a) normalisation (b) position(c) time probability density (d) position probability density

The expression $|y(x, t)|^2$ is commonly encountered in quantum mechanics, particularly in the context of wave functions. Let's analyze the provided options to determine the correct answer:

1. Understanding the Expression: The term $|y(x, t)|^2$ denotes the square of the modulus of a wave function $y$ that depends on position $x$ and time $t$. In quantum mechanics, this represents a probability density.

2. Evaluating the Options:

   • (a) Normalization: While $|y(x, t)|^2$ is related to normalization of the wave function, it is not the definition itself.
   • (b) Position: This option is not accurate; $|y(x, t)|^2$ is not a direct representation of position.
   • (c) Time Probability Density: This is misleading; $|y(x, t)|^2$ can vary with time, but it primarily represents the probability density at a given position and time.
   • (d) Position Probability Density: This accurately describes $|y(x, t)|^2$. It gives the probability density of finding a particle at position $x$ at time $t$.

Final Answer

The correct answer is (d) position probability density.