# What is the number of confined states in these potential wells?

Homework Statement:
what is is maximum and minimum number of confined states within these potential wells ?
Relevant Equations:
UL>(pi^2)(hbar^2)/8me , the condition for existence of states in the semi infinite well
hi guys
i came across this question about the maximum and minimum number of bound states that can be confined in these potential wells
1- infinite potential well
2- semi infinite potential well (from one side)
3 - finite potential well
i think i have a good idea about the minimum number of states i guess :
1- the infinite has minimum of 1 state it could always have at least one state
2 - the semi infinite if it were very shallow it could have no states so the min is 0
3 - the finite also always have at least 1 states inside no matter how shallow
is that correct.

and I am not sure what is the maximum in each and shouldn't that be dependent on the exact value of V ,
is there is a formula for that that depend on potential ?

Staff Emeritus
(1) You're surely not writing down the exact problem. "Infinite potential well" could mean many things. Most likely it means 1-dimensional infinite square well, but you shouldn't make us have to guess.

(2) You're not working the problems. You're guessing, and you're asking us if your guess is right.

• vanhees71 and patric44
Keith_McClary
Gold Member
Most likely it means 1-dimensional infinite square well, but you shouldn't make us have to guess.
The answer depends on the dimension.

• patric44
(1) You're surely not writing down the exact problem. "Infinite potential well" could mean many things. Most likely it means 1-dimensional infinite square well, but you shouldn't make us have to guess.
(2) You're not working the problems. You're guessing, and you're asking us if your guess is right.
I am sorry I should had puten more effort in presenting the problem and my attempt, so here we go :
in the following 1D potential wells as described by the figures : the question was asking to find the maximum and the minimum number of bound states confined within these systems ?
the minimum number can be obtained by looking at the transcendental equation plot for each system, i am taking about the the last two systems , since the infinite well is infinite i guess there is no max and the min is 1 correct me if I am wrong, now for the two systems: the left one is for the finite well and it shows an intersection point (represents a solution) no mater how shallow the well is . so the minimum is 1.
the right one shows no intersection up till a condition of $$UL>\frac{\pi^{2}\hbar^{2}}{8m}$$
so the min is 0.
not sure how to get the maximum number of states , is it by counting the total intersection points
or there is another approach ?