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So, why did Schrodinger put de Broglie's relation and Hamiltonian together to

achieve "particle-wave duality"? I can not find convincing scientific

reason for this.

1. Einstein and Planck showed a "successful" wave-particle duality of

light and photon. Einstein used relativistic energy-momentum to do this

[not knowing the contradiction coming from e=hf=0/0 which is

e=sqrt((cp)^2+(m0)^2c^4)=cp=

This apparently "solved" the mystery of the double slit experiment for

light. Indeed, Schrodinger managed to "explicate" this using the

uncertainty principle for light/photon. [By the way, Suntora showed that

the blackbody radiation problem is resolved by considering the light wave

used to be monochromatic waves rather than harmonic waves. So, Planck's

quantization is not needed at all.]

2. De Broglie wanted to have the same duality for any particle to

explicate the double slit experiment. Following the steps of Planck who

quantized mathematical em waves, he tried to quantize mathematical plane

waves. In stead of Einstein's relativization 0/0 of Planck's photon, he

relativized (transformed) wave "functions" not wave equations in terms of

wavenumber and frequency. [BTW this was a correct thing to do. As I have

been arguing for many years, wave functions and wave equations are not the

same thing. For example, Galilean transformation of wave functions are

wave functions but it is not the case for wave equations. But, I do not

see why it has to be Lorentz transformation rather than Galilean

transformation. The only reason seems to be because Einstein relativised

Plank's photon using Lorentz transformation. 0/0 comes from the gamma

factor which was the wrong thing to do.]

3. It turned out to be that the Lorentz transformation of plane wave

equation as "(wave number)-(wave frequency) relation" and that of

"energy-momentum relation" are mathematically the "same form. From this

"symbolic analogy", de Broglie concluded that "if there was a connection

between wave and particle, the following relation must be true:

p=(h/2pi)k and E=(h/2pi)f

where k is the wave number and f is the wave frequency." What is important

here is that de Broglie never said that there "is" a connection between

wave and particle. He said that "if" there is then it must be expressed as

the equations above. This is not to say that wave and particle are always

connected through the equations (de Broglie relation) above.

4. Schrodinger was looking for a mathematical formalism to connect

particles of Newtonian mechanics (not just a particle as de Broglie

presented) and desired wave representation of it. He represented classical

particles as Hamiltonian energy equations. Then using the hypothetical de

broglie relation namely p=(h/2pi)k, he converted Hamilton's energy

equation to the so called Schrodinger wave equation.

So, after all, Schrodinger's wave mechanics was developed upon "not the

fact but the assumption" that the wave particle duality exists in the form

of de Broglie relation. So, even today it is not clear if Schrodinger

really established a physical fact that wave-particle duality exists. He

just assumed the wave-particle duality and presented a mathematical

equation which describes such assumed duality.

This fundamental problem was never understood nor noticed. Physics

community was too busy with "harvesting " the fruits grown in the

forbidden garden. I do not see that Feynman-Landau-Lifschitz Lagrangian

formalism of QM resolved this very essential problem. Nobody really

understood what Schrodinger-Feynman-Landau-

themeselves. Worshipping of mathematical formulas is sticking its ugly

head as usual.

******************************

Akira

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