Empty Mantra of Particle Light Quanta in Photoelectricity

Grand piano as radiating atom

The story of the modern physics of quantum mechanics says that it all started with Einstein's 1905 "heuristic explanation" of the Law of Photoelectrity returning to Newton's particle view of light of frequency $\nu$  as consisting of little lumps or energy or photons of size $h\nu$, with $h$ a certain small constant today normalised to 

• $h=4,135667696\times 10^{-15}$ electronVolts per Hz.   (P)

Einstein's heuristics was met with total skepticism since light was well known to be an electromagnetic wave phenomenon precisely described by Maxwell's equations. Moreover the Law Photoelectricity of the form 

• $E = h\nu + W$          (L)

was well know long before 1905, with here $E$ electron energy in electronVolts and $W$ "release energy". In any case Einstein received the Nobel Prize for the "discovery" of (L) and not for his "heuristic explanation" of (L) based on energy quanta/photons, which nobody then believed in.  

But the Prize gave credibility to Einstein and so his particle idea of light as consisting of little lumps of energy entered as an element of the new quantum mechanics formed in the 1920s. 

Let us now explain (L) as an expression of Schrödinger's equation for Hydrogen discussed in the previous post The Real Essence of Quantum Mechanics, which is a wave equation without particles:

• $i\frac{h}{2\pi}\exp(-i\frac{E}{h}2\pi t)\Psi = H\Psi$,     (S)

where $\Psi (x,t)$ is a wave function depending on a space variable $x$ and time variable $t$ and $H$ is Hamiltonian operator with eigenvalue $E$ representing electron energy. The solution of (S) is a harmonic oscillation with frequency $\nu =\frac{E}{h}$ in Hz, which carries the connection $E=h\nu$ as connection between electron energy and frequency, with a connection to light through the line spectrum of Hydrogen with $E$ as a "beat frequency" as difference between eigenvalues. The value of Planck's constant (P) is determined to make frequency predicted by (S) fit with observation of the line spectrum of Hydrogen, thus as a calibration of (S) to fit observation, effectively determining a relation between kinetic spatial energy and potential electron energy in (S).   

We are thus led to the relation $E=h\nu$ between electron energy and light frequency from Schrödingers wave equation as an expression without need of any particle interpretation. Planck's constant $h$ appears as conversion factor between electron energy and light energy. 

Returning now to (L) we see that modulo the release energy $W$ independent of frequency, (L) is nothing but $E=h\nu$ derived from Schrödinger's equation for the Hydrogen atom, which expresses the conversion of light energy into electron energy realised in photoelectricity. No need here to speak about lumps or energy or photons as having physical realisation. The Mantra of Particle Quanta in Photoelectricity is empty. The wave equation (S) is enough. 

Yes, you can determine Planck's constant $h$ by shining light on a metal surface and observe the "stopping potential" bringing the flow of electrons produced by the light to a stop, thus measuring per electron $E$ in Volts and knowing the frequency $\nu$ determining $h=\frac{E}{\nu}$. 

The line spectrum of Hydrogen shows that a Hydrogen atom acts like a "light piano" generating a discrete spectrum of "light tones" under excitation as wave mechanics of strings. No need to believe a piano as being "quantised" just because it generates a discrete spectrum of tones. No need to believe an atom being "quantised" just because it has a discrete line spectrum. No need of "particles of energy". More on RealQM.   

Einstein as young patent clerk in 1905 with great ambitions to become a name in physics, however with little research experience, simply had to "find something" and he did. 

Planck determined a value of $h$ from assuming a high-frequency cut-off scaling with $\frac{T}{h}$ where $T$ is temperature, in the spectrum of blackbody radiation. Observing the spectrum cut-off for some temperatures $T$, allowed Planck to determine a value of $h$ up to 4 percent. Planck resorted to particle statistics of assumed quanta of smallest size $h$ to motivate the cut-off. 

Computational BlackBody Radiation gives a different view based on wave mechanics free of statistics motivating cut-off by a principle of "finite precision computation".  

Summary

RealQM and Computational BlackBody Radiation show that Planck's constant serves the following roles: 

• Conversion factor between electronic and light energy.
• Cut-off in blackbody radiation.

Nothing here says that atomic physics is particle physics. Continuum wave physics can describe the physics originally motivating introduction of particles/energy quanta. This is a relief resolving the unsolvable artificial problems coming from insisting on discreteness on small scales.