Bra-ket

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~ Paul Dirac on this page.

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The bra-ket notation is a way of life and a major religion provided by quantum mechanics and used as a form of language. An exaple of this language is the statement about your mother: Let be $\langle F|$, your mother value of happiness and let $|K\rangle$, your neighbor in her bed... we have $\langle F|$U$|K\rangle$ that means your mother is happy only and only if your neighbor is around the bed.

Rules

Do you remember Schrodinger's cat? Well is dead now and we know for sure (the horrible smell from the box) but the cat's paradox explains how this language operates. We have $\alpha$$|a\rangle$ -> Cat is alive... and $\beta$$|b\rangle$ -> Cat is NOT alive. If we assume that $\alpha$$|a\rangle$ $+$ $\beta$$|b\rangle$ $=$$|A\rangle$, the probability that the cat is alive AND dead at the same time is A. But if we operate A with the "shake the box" function(U) then the cat will always tend to die, seeing is believing. So U$|A\rangle$ -> $\beta$$|b\rangle$, in this phase we "normalized" the vector-probability A with a function (U), by the way NOT every cats tend to stay in a box for a long time but every cats tend to die as soon as the box is shaked.

Examples

• $\langle \beta |c_{1}\alpha _{1}+c_{2}\alpha _{2}\rangle =c_{1}\langle \beta |\alpha _{1}\rangle +c_{2}\langle \beta |\alpha _{2}\rangle$

Let $\langle \beta |$ be the probability of something great happening; let be $c_{1},c_{2}$ your happiness functions and let $\alpha _{1},\alpha _{2}$ be someone that will ruin your day, in theory your great day will be ruined by two different people at least, so your total hapiness depends on others as expected by physics you for sure will have two or more friends that probably will destroy your happiness... KILL THEM, KILL THE VARIABLES YOU CANNOT CONTROL!!!

• $\langle \beta |\alpha \rangle ^{*}=\langle \alpha |\beta \rangle$

Let $\langle \beta |\alpha \rangle ^{*}$ be "Start dressing from underpants" and let $\langle \alpha |\beta \rangle$ be the opposite (you start dressing from the coat), it exists a relation $\langle \beta |\alpha \rangle ^{*}=\langle \alpha |\beta \rangle$ that explein how is equal dressing from underpants or starting from the coat.

• $\langle \alpha |\alpha \rangle \geq 0$ e $\langle \alpha |\alpha \rangle =0\Leftrightarrow |\alpha \rangle =|0\rangle$

Let $\langle \alpha |\alpha \rangle$ be "Eating and not eating" then $\langle \alpha |\alpha \rangle =0\Leftrightarrow |\alpha \rangle =|0\rangle$ it means eating and not eating can be simplified as "0" that is not a zero but your own tale; eating yourself until you cannot eat anymore.

History

It seems that the language was invented by Paul Dirac, a strange person who enjoyed experimenting with dogs and little pets, usually with boxes full of poison or weapons. He knew Schrödingher quite well and moreover he knew his cat that mysteriously went missing, the language was first invented to describe the concept of life and not life at the same time. Many years passed and strangely the language was used more and more by students of physics and mathematics to send cryptic messages to each other. Soon it becames a well known language after quantum physics was invented... so many cats and so many boxes... it was $\langle Awful|Fun\rangle$ at the same time!

Internal links

• Schrodinger's cat
• Math
• Physics