Pineapple Juicer machine and her son Pineapple Juice

Last time we saw how Miss p̂ identified her son p₁ and we tried to understand the equation, p̂ |Ψ⟩=p₁|Ψ₁⟩. If you haven't already read the lovely story of Miss p̂, she would love it if you do. Here it is. 

Now we will see how she finds her child when there are more than one class sections in that school, and try to explain the equation,
p̂ |Ψ⟩= p₁ |Ψ₁⟩ + p₂ |Ψ₂⟩ + p₃ |Ψ₃⟩ + p₄ |Ψ₄⟩ + p₅|Ψ₅⟩

Last time, the school had just one class section, |Ψ₁⟩. So things were simple and easy. Now, things have changed. The school has five sections of class Ψ, that is |Ψ₁⟩, |Ψ₂⟩, |Ψ₃⟩, |Ψ₄⟩, |Ψ₅⟩. Also, last time, Miss p̂ was a human. Now she is not a human but a machine, a juicer machine which specifically makes pineapple juice.

Things to remember:


1. Miss p̂ is mother. She is a juicer machine, specifically a pineapple juicer.

2. Headmistress |Ψ⟩ is a headmistress of Ramanujan Public School.

3. The juicer machine Miss p̂ has a son- he is a juice, pineapple juice.

4. There are five sections in RP school: |Ψ₁⟩, |Ψ₂⟩, |Ψ₃⟩, |Ψ₄⟩, |Ψ₅⟩

5. Since all the children are juices, they need a glass🍷 to sit in class, otherwise they will spill out. The glass is free of cost for all the students. So when Pineapple juice is in section |Ψ₁⟩, his name is Pineapple juice 1 or p₁, when he is in |Ψ₂⟩, his name is Pineapple juice 2 or p₂. 


Scenario 1:

So one day, Miss p̂ approaches the headmistress |Ψ⟩ who still has the large bun and a large stick, and says, "dear headmistress, since it's almost weekend, we have planned a trip to Veegaland and will be leaving this evening. So I would like to pick my son Pineapple Juice early" to which the headmistress responds, "dear Miss p̂, you have to tell us his class section since we are a bigger school now". But there is a problem, Miss p̂ knows that her son Pineapple Juice is a naughty child and can be in any of the class sections. So she tells the headmistress, "could you please search all the classes since I cannot say where he has gone today". The clerk then goes and checks with the teachers of all classes and finds that her son Pineapple Juice is in class |Ψ₁⟩ and so his name is p₁. Miss p̂ takes her child and they happily leave for Veegaland.


Scenario 2:

Miss p̂ again goes to his school on next Friday and tells the headmistress, "dear headmistress, this week, we are going to Bird sanctuary, and I want to pick my Pineapple Juice early." The headmistress asks, " Okay, so in which class is he today? Miss p̂ says, "please search for him in all the sections". The clerk then finds out that Pineapple Juice is in |Ψ₃⟩ and so his name is p₃.


Scenario 3:

The next weekend, Miss p̂ again goes to the headmistress and tells her, "dear headmistress, this week we are going to see waterfalls, please bring my son so that we can leave early." The clerk then goes and he finds pineapple juice in section |Ψ₁⟩. But he is half empty! Where is the rest of Pineapple Juice? The clerk goes around and finds that the other half is in |Ψ₂⟩. He collects Pineapple Juice from both the classes and gives to his mother. That means, Pineapple Juice is both in |Ψ₁⟩ and |Ψ₂⟩.

Aaand.. that, my friends, is the property of the operators like p̂. If you are curious why Miss p is a juicer machine instead of being just a big glass of juice, that's a story for another day 😁. So don't worry if everything is not clear immediately.

(Below given is an explanation of the story explained above. If the technical details given below are heavy and don't make any sense to you, feel free to skip and enjoy the story part alone).

Now some Physics:


When you operate some operator p on a state, it never gives an exact answer in quantum mechanics. It can be p₁, p₂ or p₃ or more depending on the state in which the measurement is made. The answer can even be a combination of these states, and that make things even murkier. 

Want to see how much murkier? Okay let me spoil the fun. The equation you saw above is still incomplete.
p̂ |Ψ⟩= p₁ |Ψ₁⟩ + p₂ |Ψ₂⟩ + p₃ |Ψ₃⟩ + p₄ |Ψ₄⟩ + p₅|Ψ₅⟩

The correct equation would be:

p̂ |Ψ⟩= a p₁ |Ψ₁⟩ + b p₂ |Ψ₂⟩ + c p₃ |Ψ₃⟩ + d p₄ |Ψ₄⟩ + e p₅|Ψ₅⟩

That is definitely complicated 😁. Let's save the explanation for another day again! 

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