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When using the time-independent Schrodinger equation and finding a wave function $\psi(x)$ for a given potential $V(x)$ is there a consistent way to plot these two objects on the same image that takes into account the differences in units and then gives you a visual way to see how various wave functions, e.g., with different eigenvalues $E_n$, behave in the same potential that is more meaningful than the "collages" that are floating around (see picture below)?

wavefunction-potential-image

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  • $\begingroup$ This gives a false impression , such plots are useful for tunneling explanations hyperphysics.phy-astr.gsu.edu/hbase/quantum/barr.html , the wavefunction should be falling within the barrier $\endgroup$ – anna v Oct 1 at 4:29
  • $\begingroup$ Well, the requirement is that the probability is falling within the barrier, and the green curve actually agrees with that. So what we are talking about here is making the visualization helpful. I would either (a) choose the phase of each eigenfunction such that their tails all looked the same (which will make their slopes at $r=0$ alternate in sign) or (b) plot the probability rather than the wavefunction. $\endgroup$ – dmckee Oct 1 at 17:58

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