[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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