Consider an electron in a semi infinite potential well ie...

Consider an electron in a semi-infinite potential well, i.e. the potential energy function is given by: U(x) = { (∞, when x < 0), (0, when 0 ≤ x ≤ L), (U₀, when x > L) } a) Find out the continuity conditions of the wave function and its derivative at x = 0 and x = L when the electron for the total energy E, E < U₀ holds. b) Find out the energy quantization condition in this case. Solve for the ground state energy of the electron (e.g. graphically) when L = 1 Å and U₀ = 35 eV. In how many different bound energy eigenstates can the electron be? The correct equation for part (a) is: c₊ + c₋ = 0 c₊e^(ipL/ℏ) + c₋e^(-ipL/ℏ) = d₋e^(-αL) ((ip/ℏ))(c₊e^(ipL/ℏ) - c₋e^(-ipL/ℏ)) = -d₋αe^(-αL)

Transcript

00:01 So here we are having the following potential which is represented by the v of x and given the boundary conditions are given which is v of x is equals to minus v0 when x mod is less than l and 0 when x mod is greater than l.

00:19 So in this example we can set at the origin of x x x is versus at the center of the well.

00:33 So by doing so potential is symmetric about x is equals to zero and given rise to the parity so for a finite well two cases must be distinguished corresponding to the positive and negative value of energy so this will be it is possible for the particle to be bound so particle to be bound and hence is in a bound state one where e is greater than zero so the particle is unconfined and corresponding to the scattering problem so the latter can will only briefly discuss so here we can say that the cases for this will be here this is oh let's say this is the x here this is 5 1 here when it is square of this 5 1 square so the graph will be somewhat like this l here l here it is x if it is if it is it is 5 2 then a graph will be in this way l here x here if it is square of that 5 2 the graph will be in this way here l is x and if it is 5 3 for 5 3 the graph will be somewhat like this where l is here x here and if it is square of 5 3 then the graph will be somewhat like this l here x here so we can say that we are having the state so the system is bound to v0 is less than equals to e less than 0 so from here we can say that when mod of x is less than l so we can say that this will be minus h divided by 2m curly square divided by a curly x square si of x minus v0 si of x this will be equals to minus mod of e si of x and we can say that this will be minus h squared divided by 2m curly square divided by a curly x square which will be equals to minus e summation of si of x so from here we can say that binding energy is represented by e or we can say that mode of e of the particle is in the root of e is equal to minus e...

Question

Please give Ace some feedback