I Proving the Schrodinger Equation

thegroundhog
Messages
16
Reaction score
10
TL;DR Summary
How were scientists able to do experiments to prove that the Schrodinger equation was correct?
How did scientists prove the accuracy of Schrodinger's equation to describe the behaviour of subatomic particles, especially in the 1920s? How do you monitor an electron's momentum and position when they are so small? Also, if the Schrodinger equation just describes probabilities, is the accuracy of the experimenting based on doing the same measurements over and over to make sure the probabilities are correct (in the same way to check the heads/tails probability of a coin, the more measurements the better, as it will tend towards 50%)?
 
Physics news on Phys.org
thegroundhog said:
Summary:: How were scientists able to do experiments to prove that the Schrodinger equation was correct?

How did scientists prove the accuracy of Schrodinger's equation to describe the behaviour of subatomic particles, especially in the 1920s? How do you monitor an electron's momentum and position when they are so small? Also, if the Schrodinger equation just describes probabilities, is the accuracy of the experimenting based on doing the same measurements over and over to make sure the probabilities are correct (in the same way to check the heads/tails probability of a coin, the more measurements the better, as it will tend towards 50%)?
You probably need to read the history of QM to clarify the exact sequence of events. In modern QM, the Schrodinger equation can be derived from some expected properties of the time evolution operator: see, for example, Modern Quantum Mechanics by J..J. Sakurai.

The acid test is not direct measurements of an electron, but the prediction of the atomic spectra for hydrogen etc. In this case, even the different energy levels themselves are not measured directly but inferred from the atom's spectrum (i.e. the measurement is of the wavelength (or frequency) of the emission and absorption spectrum).
 
  • Like
Likes bhobba and vanhees71
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...

Similar threads

Back
Top