Which of the following statements on the atomic wave function `Psi` is not correct?

Options

A. `Psi` may be a real valued wave function
B. `Psi` may be in some cases be a complex function
C. `Psi` has a mathematical significance
D. `Psi` proportional to the probability of finding an electron

Answer

To determine which statement about the atomic wave function \( \Psi \) is not correct, we will analyze each option based on the properties of wave functions in quantum mechanics.

### Step-by-Step Solution:

1. **Understanding the Wave Function \( \Psi \)**:
The wave function \( \Psi \) describes the quantum state of a particle, such as an electron in an atom. It contains information about the probability distribution of the particle's position.

2. **Components of the Wave Function**:
The wave function can be expressed in two parts:
- **Radial Contribution**: This part, denoted as \( R_{nl}(r) \), describes how the wave function varies with the distance from the nucleus.
- **Angular Contribution**: This part, denoted as \( Y_{l,m}(\theta, \phi) \), describes the shape of the wave function in terms of angles.

3. **Analyzing Each Statement**:
- **Option 1**: "Psi may be a real valued wave function."
- This statement is correct. The wave function can be either real or complex depending on the quantum state.

- **Option 2**: "In some cases, Psi may be a complex function."
- This statement is also correct. The wave function is often complex, particularly in the case of non-stationary states.

- **Option 3**: "Psi has a mathematical significance only."
- This statement is correct. While the wave function is a mathematical construct, it has physical significance in terms of probability distributions.

- **Option 4**: "Psi is proportional to the probability of finding an electron."
- This statement is **incorrect**. The probability density of finding an electron is given by \( |\Psi|^2 \), not \( \Psi \) itself. The wave function \( \Psi \) can be complex, and thus cannot be directly equated to probability.

4. **Conclusion**:
The statement that is not correct is **Option 4**: "Psi is proportional to the probability of finding an electron."