[plt-scheme] Currying and physics
Sorry. Because I am dont look much at parentheses I wrote '(;' meaning '):' of course,
Jos
----- Original Message -----
From: Jos Koot
To: Gregory Woodhouse
Cc: plt-scheme at list.cs.brown.edu
Sent: Friday, January 02, 2009 9:46 PM
Subject: Re: [plt-scheme] Currying and physics
Ok, I am sure you are sure are familiar with the mather (:.
You did show a nice example of currying, no doubt about that.
Jos
----- 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.
Jos
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