consider a 1-D problem where a charged particle travels along +x with a bound state energy.(adsbygoogle = window.adsbygoogle || []).push({});

the vertical potential energy axis is displaying information about the forcethe particle's axis of motion. is this correct?that is parallel to

so then this would be an accurate representation?

where blue arrows represent E-field and the direction of force felt by a (+) test particle.

$$\lim_{ε→0}$$

so if it's just the force component that is parallel to the direction of motion that determines whether the particle is in a bound state or scattering state, please confirm the following analysis is correct:

consider a charged ideal parallel plate capacitor:

(where the fields do not leak outside the plate area)

positive test particle enters orthogonally to the field. but because the acting force on the particle is orthogonal to its motion, the effective potential energy for determining bound vs scattering state, is zero.

but at the end, the particle has a velocity component parallel to the force, so it has a chance to be bound or scattered along this vertical axis.

is this correct?

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# Potential energy term in Schrodinger's equation?

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