Question

Sketch$\mathit{\psi }\mathbf{\left(}\mathbf{x}\mathbf{\right)}$ . Would you expect this wave function to be the ground state? Why or why not?

Short answer

The wave function cannot be in the ground state as it has two types of anti-nodes.

Step-by-step solution

Significance of a wave function 

The wave function is described as the properties of a particular wave that mainly satisfies the wave property. However, it also describes a particle’s wave characteristics.

Sketching the function

The wave function has been sketched below:

Here, in this diagram, it has been observed that at the midpoint, the wave function is zero. Apart from that, at the first and the final segment of the distance, the wave function is at its peak.

Determination of the state of the wave function

According to the sketch of the wave function, the wave function cannot be in the ground state as it has two types of anti-nodes. Hence, the function should be at the first excited state.

Thus,

The wave function cannot be in the ground state as it has two types of anti-nodes.