(adsbygoogle = window.adsbygoogle || []).push({}); Problem

A particle in one dimension is subjected to a constant force derivable from

[tex]V = \lambda x[/tex]

Is the energy spectrum continuous or discrete? Write down an approximate expression for the energy eigenfunction specified by [tex]E[/tex].

Solution attempt

We have an unbound state, so we would have acontinuousenergy spectrum. Well, I was thinking of something along the lines of [tex]\psi(x)=e^{-f(\lambda) x} \sin (x-e^{-h(\lambda)})}[/tex] for the region [tex] x < E/\lambda[/tex] (of course, for [tex]x > E/\lambda[/tex], we need an exponentially decreasing function); I chose this function based on the following:

1. The function needs to increase exponentially as we go farther left, because the energies are greater than the linear potential by a greater degree.

2. The zeroes need to be bunched together closer as [tex]x\rightarrow -\infty[/tex], because the particle is more energetic here.

Above, [tex]f(\lambda), g(\lambda)[/tex] are positive functions for [tex] \lambda > 0 [/tex].

Is the above correct?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear Potential Question

**Physics Forums | Science Articles, Homework Help, Discussion**