How operator p identified her child

Now we are wondering about our equation

p̂ |Ψ⟩=p₁|Ψ₁⟩

Let's imagine |Ψ⟩ is the headmistress of Ramanujan public school. Now what about the symbols like | and ⟩? Well, they are the symbols of her authority as a headmistress. One is her large bun and the other is a large stick.

One day, a parent named Ms. p̂ approaches the headmistress |Ψ⟩. Now why does p has a hat on her head. Let's say that is so since p "goes with an appeal to |Ψ⟩". So whoever has a request gets a hat on head 😉.

What does she say to the headmistress? She says, "dear headmistress, since today is the last working day, we have planned a trip to Veegaland and will be leaving this evening. And so I want to pick my son."

The school has hundreds of children and the headmistress |Ψ⟩ wouldn't know who is the child of Ms. p̂. So she asks, "what is his name?" Ms. p̂ tells her, his name is p₁. A clerk then goes to the class and picks a boy named p₁, the son of Ms. p̂.

And this is how Ms. p̂ is able to pick her child from his class.

What is the physical reality we understand from this oversimplified example? p̂, (which is read as operator p), operates on (goes with an appeal to)

|Ψ⟩ which is a representative of the system (the headmistress of the school). p̂ modifies the system to extract the value of p in the only existent state |Ψ₁⟩ (Ms. p̂ appeals to the principal to bring her son from the only class of the school).

The reality is much more complicated from this oversimplified example. When we are given p̂, the value of p in state Ψ₁ is not known to p̂. It is something we calculate. That means Ms. p̂ don't know the name of her son. So she can't tell the headmistress what is the name of her son. (It is more like the principal sees the parent and hands over an appropriate child to her!) She just knows that her son is in that school. Also, the school happens to have only one class, i.e., Ψ₁.

The immediate question would be, how does Ms. p identify her child in a school having many classes? That's a topic for another day!