I was told that for a finite potential well of depth $V_{0}$ and length(spread) $L$, the number of bound states($n$) that we could get for a particular $V_{0}$ is given by the equation- $$n=\left \lceil{\sqrt{8mV_{0}}L/h} \right \rceil$$How do I arrive at this point after looking at the graphs associated with the finite well problem? My guess is that we've to arrive at $n<\sqrt{8mV_{0}}L/h$, but I don't know how should I start so that I get a relation for the number of bound states in this problem. Can someone help me out in this, cuz I'm fairly new to QM!
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$\begingroup$ Related: physics.stackexchange.com/questions/60123/… $\endgroup$– Tobias FünkeCommented Jan 19, 2021 at 16:26
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$\begingroup$ Ok, but the expression I have, and the one used in your link are different! $\endgroup$– AntManCommented Jan 19, 2021 at 17:52
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2$\begingroup$ Sorry but your $n$ is exactly the same as the $N$ in the linked answer. $\endgroup$– ZeroTheHeroCommented Jan 19, 2021 at 19:27
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