[plt-scheme] Currying and physics

From: Jos Koot (jos.koot at telefonica.net)
Date: Fri Jan 2 15:46:03 EST 2009

Ok, I am sure you are sure are familiar with the mather (:.
You did show a nice example of currying, no doubt about that.

  ----- Original Message ----- 
  From: Gregory Woodhouse 
  To: Jos Koot 
  Cc: PLT List 
  Sent: Friday, January 02, 2009 4:48 PM
  Subject: Re: [plt-scheme] Currying and physics

  Yes, I did. I even called it P!

  On Jan 2, 2009, at 1:16 AM, Jos Koot wrote:

    You probably mean (linear) momentum. Position can be represented by an operator (function, functional) Ψ -> xΨ. The probability to find the particle at position x at time t is:
    integral over x of Ψ*(x,t) x Ψ(x,t) divided by
    the integral over x of Ψ*(x,t) Ψ(x,t),
    where Ψ* is the complex conjugate of Ψ.
    In this case momentum is represented by the function Ψ -> (iħ/2π)(δΨ/δx).
    You could have choosen Ψ(x)=1/(1+x^2) as a function with finite norm,
    or in three dimensions 1/(1+x^2+y^2+z^2)
    In practice wave functions are often represented by time independent vectors (called kets) in a Hilbert space.
    Which functions Ψ are to be included in this space is determined by the law of conservation of energy. In quantum mechanics this law says: HΨ=EΨ, where H is the so called Hamiltonian (an operator representing energy) and E a real number. The equation must be solved for both Ψ and E (and the solution usually consists of an infinite number of pairs Ψ and E) By using the symmetry properties of the system being studied, many parts of the integrals can be simplified to summations.

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