Which one of the following conditions incorrect for a well behaved wave function `(varphi)` ?

Options

A. `varphi` must be finite
B. `varphi` must be single valued
C. `varphi` must be infinite
D. `varphi` must be continuous

Answer

To determine which condition is incorrect for a well-behaved wave function (denoted as ψ), we need to analyze the properties that a wave function must satisfy. Here are the steps to solve the question:

### Step-by-Step Solution:

1. **Understanding Wave Function Properties**:
A wave function must satisfy certain conditions to be considered well-behaved. The common properties include:
- It must be **single-valued**.
- It must be **finite**.
- It must be **continuous**.

2. **Evaluating Each Option**:
- **Option 1: ψ must be finite**:
A wave function must not approach infinity at any point in space. If it does, it would not be physically meaningful. Therefore, this condition is correct.

- **Option 2: ψ must be single-valued**:
For each point in space, the wave function must have only one value. This means that for a given position, there cannot be two different values of ψ. This condition is also correct.

- **Option 3: ψ must be infinite**:
This statement suggests that the wave function can take on infinite values. However, a well-behaved wave function cannot be infinite at any point; it must remain finite. Therefore, this condition is incorrect.

- **Option 4: ψ must be continuous**:
A wave function must not have any discontinuities. It should change smoothly without any jumps. This condition is also correct.

3. **Identifying the Incorrect Condition**:
From the evaluation of the options, we find that the only incorrect condition is:
- **Option 3: ψ must be infinite**.

### Conclusion:
The incorrect condition for a well-behaved wave function is that ψ must be infinite. Thus, the correct answer is **Option 3**.

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