- #1
nshrikhande
- 4
- 0
Hi All,
I'm nk and new to your forum!
Pl., excuse my editing skills just this post. I'll catch on fast-promise!
It is known that "In physics and chemistry,
wave–particle duality is the concept that all matter exhibits
both wave-like and particle-like properties."-Reference,
http://en.wikipedia.org/wiki/Wave–particle_duality
However, I have not seen a math expression relating both
aspects of EM wave-particles. So, I deviced the following:
Let a photon be discrete represented by an ON-OFF beahaviour.
This is our typical periodic step function or even the Dirac-
delta function expressed periodically. Physically it means that
the photons energy OR sheer existence is periodic in this
fashion.
From the Fourier series (http://en.wikipedia.org/wiki/Fourier_series)
we know also that:
f(x) = A0 + Sum[n:0 to infinity] { An*cos(n*X) + Bn*sin(n*x) }
Erwin Kreyszig, Fourier series, Integrals and Transforms
Chapter 10, Edition 8th.
where, f(x) (photon) is a peicewise continuous function which is discrete in
it's totality.
Thus LHS = discrete entity and RHS = continuous enity !
LHS = RHS simultaneously, ontologically speaking.
Any opinions on this approach to quantify, with assumptions, the QM problem
of wave-particle duality?
NK.
I'm nk and new to your forum!
Pl., excuse my editing skills just this post. I'll catch on fast-promise!
It is known that "In physics and chemistry,
wave–particle duality is the concept that all matter exhibits
both wave-like and particle-like properties."-Reference,
http://en.wikipedia.org/wiki/Wave–particle_duality
However, I have not seen a math expression relating both
aspects of EM wave-particles. So, I deviced the following:
Let a photon be discrete represented by an ON-OFF beahaviour.
This is our typical periodic step function or even the Dirac-
delta function expressed periodically. Physically it means that
the photons energy OR sheer existence is periodic in this
fashion.
From the Fourier series (http://en.wikipedia.org/wiki/Fourier_series)
we know also that:
f(x) = A0 + Sum[n:0 to infinity] { An*cos(n*X) + Bn*sin(n*x) }
Erwin Kreyszig, Fourier series, Integrals and Transforms
Chapter 10, Edition 8th.
where, f(x) (photon) is a peicewise continuous function which is discrete in
it's totality.
Thus LHS = discrete entity and RHS = continuous enity !
LHS = RHS simultaneously, ontologically speaking.
Any opinions on this approach to quantify, with assumptions, the QM problem
of wave-particle duality?
NK.