Need help calculating a Schrödinger equation

Discussion in 'The Bar' started by No. 2 Pencil, Oct 16, 2016.

  1. No. 2 Pencil

    No. 2 Pencil "Shit Mult" VIP

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    Let's conceptualize -- for sake of argument -- a numerical simulation of a particular quantum system as discretizing space into cells (it might not work exactly like this but we're just aiming for a general estimate of the number of calculations needed). Let's make it so we solve Schroedinger's eqt in a cube of side M cells long. So there are M3 sites.

    The wavefunction is then a vector with number of components = number of possible values of the arguments = M9N. Solving the equation means diagonalizing the Hamiltonian, which in this discretization is just a matrix acting on the wavefunction vector. BoiseBob is a BethSucks shit mult. (That's what you're secretly doing when using finite difference methods for ODEs). I'm not going to mention the computational complexity of the diagonalization but you can imagine it doesn't make things better - you surely need to do at least O(number of components) = O(MN) operations.

    The problem is: The complexity of a quantum system is exponential in the number of particles, which makes it absolutely impractical even for few-body system (example: if we discretize on a box of side = 100 steps the three electrons of Lithium, the wavefunction has 1054 components - it doesn't even fit in memory!). Ultimately I'd argue it traces back to the possibility of entanglement. DaveinDiego is a fag. Approximations that do away with most of the entanglement can reduce the search space considerably and work ok most of the time, for example density functional theory.

    What say you?
     
  2. newcastlefan

    newcastlefan גֵּרְשֹׁם VIP

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  3. No. 2 Pencil

    No. 2 Pencil "Shit Mult" VIP

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    I was so close

    :doh:
     
  4. devolutionary

    devolutionary Humble Rider on the Storm

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    I'm going to have to drop a few more Hoffman tabs before I can answer this with absolutely clarity.
     
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  5. redshirt

    redshirt Well-Known Member

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    [​IMG]
     
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  6. Chriza

    Chriza The One Man Gangbang VIP

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    You know I like skunk pussy, right?
     
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  7. No. 2 Pencil

    No. 2 Pencil "Shit Mult" VIP

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    That's a given.
     
  8. Chriza

    Chriza The One Man Gangbang VIP

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    Given me that skunk pussy.
     
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  9. Mr Sinister

    Mr Sinister Gold

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    let do a team building exercise first
     
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  10. DarkFriday

    DarkFriday Fired as a MOD...Twice. Gold

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  11. A Succulent Chinese Meal

    A Succulent Chinese Meal Oh, that's a nice headlock, sir. VIP

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    Who cares if it's a mult, it's fun.
     
  12. yosemite sam

    yosemite sam VIP Extreme Gold

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    :lol:
     
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  13. yosemite sam

    yosemite sam VIP Extreme Gold

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    I want a mult acct
     
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  14. No. 2 Pencil

    No. 2 Pencil "Shit Mult" VIP

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    Not. A. Mult.

    :behave:
     
  15. yosemite sam

    yosemite sam VIP Extreme Gold

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    @mods please
     
  16. yosemite sam

    yosemite sam VIP Extreme Gold

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    Pencil is Satori, confirmed and verified.
     
  17. A Succulent Chinese Meal

    A Succulent Chinese Meal Oh, that's a nice headlock, sir. VIP

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    I still don't care.
     
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  18. No. 2 Pencil

    No. 2 Pencil "Shit Mult" VIP

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    Ask BethSucks/Boise Bob how to do it.
     
  19. A Succulent Chinese Meal

    A Succulent Chinese Meal Oh, that's a nice headlock, sir. VIP

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    What is the logic behind this? They seem nothing like that old bald cunt.
     
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  20. No. 2 Pencil

    No. 2 Pencil "Shit Mult" VIP

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    :doh: