# Hydrogen atom in plane wave electronic field

• Quantum River
In summary, the conversation discusses the motion equation of an electron in a Coulomb field and a plane wave electronic field. The equation is d^2 x/ dt^2=-1/x^2+cos t, where x is the coordinate and t is the time. The possibility of solving the equation exactly is also mentioned, but it is noted that it may be complex. The equation is useful in physics, but the speaker doubts its physical sense. They clarify that the -1/x^2 term represents the Coulomb force from the Hydrogen nucleus and the cos t term represents a simplification of the electric field.

#### Quantum River

We just consider one dimensional case and the classical method.
Then the motion equation of the electron in Coulomb field and the plane wave electronic field is
d^2 x/ dt^2=-1/x^2+cos t. (x is the coordinate and t is the time. )
How to solve the equation exactly?
We don't consider such cases as the electron collision with the Hydrogen nucleus.

Quantum River

That's a badly non-linear equation. Do you have any reason to think that it has an exact solution?

The equation is a one-body problem. We can't solve the three-body problem, but maybe the one-body problem is always solvable, even if the answer could be highly complex.
The equation is very useful in physics. So I want to solve it exactly.
Quantum River

d^2 x/ dt^2=-1/x^2+cos t.

The left hand side has dimensions of acceleration, while the right-hand side has a mixture of 1/L2 and cos t, which is dimensionless, so the t would have to be mutiplied by 1 (1/T), where T is time.

if the equation was

d^2 x/ dt^2=-(cos t)/x^2, then it could be readily solvable, but I doubt it makes physical sense.

The part of -1/r^2 actually means the Coulomb force generated by the Hydrogen nucleus.
The part of cos t is the simplification of e*E0*cos (omega*t).
e is the electric charge of the particle;
E0 is the electric field intensity.
cos t is the change of the electric field.
Quantum River

## 1. What is a hydrogen atom in a plane wave electronic field?

A hydrogen atom in a plane wave electronic field refers to a theoretical model in which a hydrogen atom is exposed to a uniform, oscillating electric field. This field represents the interaction between the atom and an external electromagnetic wave.

## 2. What is the significance of studying a hydrogen atom in a plane wave electronic field?

Studying a hydrogen atom in a plane wave electronic field allows scientists to better understand the behavior and properties of atoms in the presence of external electromagnetic fields. This has important implications in various fields such as quantum mechanics, atomic and molecular physics, and materials science.

## 3. How is a hydrogen atom affected by a plane wave electronic field?

In a plane wave electronic field, a hydrogen atom experiences a force that causes it to oscillate and absorb energy from the field. This results in changes in the atom's energy levels and can lead to phenomena such as resonance and ionization.

## 4. Can a hydrogen atom in a plane wave electronic field be observed experimentally?

Yes, a hydrogen atom in a plane wave electronic field can be observed using techniques such as spectroscopy or laser-based experiments. These experiments allow scientists to measure the changes in the atom's energy levels and study its behavior in the presence of the field.

## 5. How does the behavior of a hydrogen atom in a plane wave electronic field differ from that in a static electric field?

In a static electric field, a hydrogen atom experiences a constant force and does not absorb energy from the field. However, in a plane wave electronic field, the atom experiences an oscillating force and can absorb energy, leading to different behaviors and energy level changes.