Can the Potential Energy of an Electron in a Hydrogen Atom be Measured?

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Discussion Overview

The discussion revolves around the measurement of the potential energy of an electron in a hydrogen atom, specifically questioning how this measurement can be achieved given the theoretical framework of quantum mechanics. The scope includes theoretical considerations, experimental implications, and mathematical challenges related to the Schrödinger equation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that the potential energy of an electron in a hydrogen atom is a definite quantity at a given point, questioning how it can be measured.
  • Others argue that while one cannot directly measure the potential energy at a specific point, experimental results such as binding energy and energy levels of hydrogen provide indirect validation of the potential energy expression V = -e^2/r.
  • A participant requests clarification on the term "BE," leading to a discussion where "binding energy" is identified as the relevant concept, specifically relating to ionization energies of hydrogen atoms.
  • There is a challenge regarding the solvability of the Schrödinger equation when the potential energy is unknown, with some suggesting that if the Hamiltonian is not fully defined, it cannot be solved for its eigenstates.
  • Another participant counters that while eigenstates are known, the potential energy function U(x) remains unspecified.

Areas of Agreement / Disagreement

Participants express differing views on the measurement of potential energy and the implications of the Schrödinger equation. There is no consensus on how to approach the measurement or the solvability of the equation with an unknown potential energy.

Contextual Notes

Limitations include the dependence on definitions of potential energy and binding energy, as well as unresolved aspects of the Schrödinger equation in the context of unknown potentials.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, particularly in relation to atomic physics and the measurement of potential energies in quantum systems.

batsan
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It is known that the potential energy of electron in the hydrogen atom is completely definite quantity, for given point . How we can measure it?
 
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"How we can measure it?" You can't place an electron at point r to measure
-e^2/r, but there are other ways to measure that V=-e^2/r is correct.
It leads to the experimental BE and energy levels of hydrogen and to the correct experimental e-p scattering.
This can be considered a measurement that V= -e^2/r is correct.
 
Can you post me some links for this problem.
What is BE? May be Bose-Einstein?
How we can solve Schrödinger equation which have given wave function , but unknown pot. energy?
Thanks!
 
batsan said:
How we can solve Schrödinger equation which have given wave function , but unknown pot. energy?
Thanks!

I'm no expert on QM, but isn't the answer to this question simply, "you...can't!" I mean, if the Hamiltonian is not fully-defined, then you can't solve for its eigenstates.
 
Last edited:
Eigenstates are known. Unknown is only U(x).
 
batsan said:
What is BE?

I think Meir means "binding energy", that is, measurements of the ionization energies of hydrogen atoms.
 
Thanks!
Of course, it's "binding energy". I didn't guess right.
 

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