Question

\(\psi(x,y,z)\) describes the wavefunction of a particle. The probability of finding the particle between \(x\) and \(x+dx\), \(y\) and \(y+dy\), and \(z\) and \(z+dz\), can be expressed as

• A. \( \psi^*(x,y,z) \psi(x,y,z) \)
• B. \( |\psi(x,y,z)|^2 \, dx \, dy \, dz \)
• C. \( \psi^*(x,y,z) \psi(x,y,z) \, dx \, dy \, dz \)
• D. \( \int_{-\infty}^{\infty} \, dx \int_{-\infty}^{\infty} \, dy \int_{-\infty}^{\infty} \, dz \, \psi^*(x,y,z) \psi(x,y,z) \)

Hint:

The probability of finding a particle in a given region is the square of the wavefunction's magnitude, \( |\psi(x, y, z)|^2 \).

Answer 1

The Correct Option is B, C

Step 1: Understanding the wavefunction.
The wavefunction \(\psi(x, y, z)\) of a particle gives the probability amplitude. The probability density is given by \( |\psi(x, y, z)|^2 \), which represents the likelihood of finding the particle in a given small volume element \(dx \, dy \, dz\). Thus, the probability of finding the particle between \(x\) and \(x+dx\), \(y\) and \(y+dy\), and \(z\) and \(z+dz\) is \( |\psi(x, y, z)|^2 \, dx \, dy \, dz \).

Step 2: Conclusion.
The correct answer is (B).