Pseudo-Quantum Mechanical description of Birthday wishes

This is what 3 years of Physics can do to you:


9:56 PM Naveen: why the deja vu suddenly?
me: What is the deja vu?
Torus and 16D compact manifold?
Naveen: yeah
remembering something that had happened in the past
9:57 PM actually it is slightly different
9:58 PM but sounds pseud all the same, so used it :)
me: Ah, okay
I understand.
Nothing, generally
Naveen: oh :)
ok
me: exp( -i H (-2:03:00) / \hbar ) | Happy Birthday >
9:59 PM Naveen: :D
exp( -i H (-2:04:00) / \hbar ) | Thank You >
10:01 PM me: \hat{B} | Naveen >
Oops
10:02 PM exp( -i H (-2:03:00 ) / \hbar ) \hat{B} |Naveen>
Where \hat{B} is the bumping operator
Naveen: he he :D
10:03 PM exp( -i H (-2:03:00 ) / \hbar ) \hat{R} |Naveen>
where \hat{R} is the run operator
ooops
exp( -i H (-2:03:00 + \epsilon ) / \hbar ) \hat{R} |Naveen>
aiyyo,
exp( -i H (-2:03:00 - \epsilon ) / \hbar ) \hat{R} |Naveen>
10:07 PM me: exp( -i H (-2:00:00 ) ) exp ( \alpha a\dagger - \alpha*a ) |Akarsh>
10:08 PM Where \alpha is chosen so that my probability distribution shifts right in front of where you will be standing after the time delay
[BTW, the time is decreasing because the time to 12:00 midnight is decreasing]
[You should use that appropriately, at least to some approximation]
10:12 PM me: BTW the exp ( \alpha... ) stuff is called the Displacement operator
And it is the operator that performs phase space translations
Naveen: ah... nice
10:13 PM me: /me enjoys the power of quantum operators that can teleport him
|Akarsh>|Naveen>
Now I've switched to the interaction basis. I shall soon apply the bumping operator
10:14 PM Naveen: let us see
10:15 PM exp( -i H (-2:03:00 ) ) exp ( -\alpha a\dagger + \alpha*a ) |Akarsh>
oops
exp( -i H (-2:03:00 ) ) exp ( -\alpha a\dagger + \alpha*a ) |Naveen>
10:16 PM what will you do now
and
10:17 PM me: Oh no.
I shall delocalize myself by squeezing myself in the p quadrature
S|Akarsh>
10:18 PM Where S is the squeezing operator, chosen so that it makes \Delta p very small
Naveen: |lightcone> = exp( -i H (00:00:28 ) ) exp ( -2\alpha a\dagger + 2\alpha*a ) |kstar>
me: Now wherever you run, you can't escape.
[Please add appropriate time evolution operators]
Naveen: |lightcone> = exp( -i H (00:00:28 ) ) exp ( -2\alpha a\dagger + 2\alpha*a ) |kstar>
10:19 PM me: Look - I'm delocalized now.
That won't save you
10:20 PM Naveen: S^{-1} |lightcone> = exp( -i H (00:00:28 ) ) exp ( -2\alpha a\dagger + 2\alpha*a ) |kstar>
10:21 PM what do you say for that?
me: Wait, how does that help?
10:22 PM Ah... ok, you're delocalizing yourself as well
Naveen: yeah
:P
me: But that won't help, because I can still interact with you
Naveen: but not effectively
me: Both of us are delocalized, so there's a LOT of overlap
Doesn't matter
Enough for me to apply bumping operator
Naveen: no effective overlap
PS|kstar>
10:23 PM me: ^^ What are PS?
10:24 PM Naveen: P_{z}S^{-1}|lightcone>
where P is the projection on the x-y plane
and P_{z} is the projection on the z axis
10:25 PM then you will be smeared on the x-y plane
and I will be stretched on to the z-axis
and there will be only one point of overlap
and you cant fit your foot(that too delocalized :P) into a point
10:26 PM me: Hmm
Look, you don't have rights to operate on my wavefunction
It's mine. I choose to do what I want with my state.
10:27 PM You have right over your state.
If you want to collapse onto the X-Y plane, you're welcome to do that - but you shouldn't be doing that to me.
You can at most produce a field which would force me to apply a certain operator on my state
10:28 PM Naveen: basically, I didnt say anything about the time evolution operators
me: Eh?
Naveen: I will do that when we interact
then I will have some effect on you
10:29 PM remember that \epsilon ?
that is why that was there
so that I can have some control over your wavefunction
me: Hmm, I don't understand.
Okay, let me withdraw from the game
10:30 PM Naveen: ok...
me: a|kstar>

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