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

• patric44
In summary: The answer depends on the dimension.(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.
patric44
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 ?

(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
Vanadium 50 said:
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
Vanadium 50 said:
(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 ?

## 1. What is the definition of a confined state in a potential well?

A confined state in a potential well refers to a quantum state in which a particle is confined or trapped within a certain region of space due to the potential energy barrier created by the well. In other words, the particle is unable to escape from the well unless it gains enough energy to overcome the potential barrier.

## 2. How is the number of confined states determined in a potential well?

The number of confined states in a potential well is determined by the shape and depth of the potential well. The higher the potential barrier, the fewer confined states there will be. The number of confined states can also be affected by the mass of the particle and the width of the well.

## 3. What is the relationship between the number of confined states and the energy levels in a potential well?

The number of confined states corresponds to the number of energy levels in a potential well. Each confined state has a specific energy level, and as the number of confined states increases, so does the number of energy levels. This relationship is known as the quantization of energy in quantum mechanics.

## 4. Can the number of confined states change in a potential well?

Yes, the number of confined states in a potential well can change if the shape or depth of the well is altered. For example, if the potential barrier is lowered, more confined states may be able to exist within the well. Additionally, if the well is made shallower, some previously confined states may no longer be confined.

## 5. How does the number of confined states affect the behavior of particles in a potential well?

The number of confined states can greatly influence the behavior of particles in a potential well. For example, particles can only occupy a certain number of confined states at a given energy level, which can affect their movement and interactions with other particles. Additionally, the number of confined states can determine the stability and lifetime of a particle within the well.

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