Lecture 10 - Finite Square Well.pdf-Toda...
Lecture_10_-_Finite_Square_Well.pdf-Today (1) Review of time dependent
Showing 1-5 out of 36
Lecture 10 - Finite Square Well.pdf-Today (1) Revi...
Lecture_10_-_Finite_Square_Well.pdf-Today (1) Review of time dependent
Lecture 10 - Finite Square Well.pdf...
Lecture_10_-_Finite_Square_Well.pdf-Today (1) Review of time dependent
Page 1
(1) Review of time dependent Vs time independent
Schrodinger eqtn
(2) When is it appropriate to use the infinite square well
(3) The finite square well and its solution
In this course, the reason why we always solve the
time independent
(TISE) Schrodinger eqtn is because
V(x,t) is ALWAYS time independent. In a more advance course,
you learn to deal with time dependence in the potential.
The infinite square well is the SIMPLEST physics system…
Simpler than the finite square well for instance

Page 2
O.k., how do we go from the time dependent Schrodinger eqtn to the time
independent one (TISE)?
We need to use separation of variables!
We first assume a separable soln form :
Plug it in and we get:
We divide both sides by
and get 2 eqtns:
Only depends on x
Only depends on t
How can something depending only on
and something depending only on
be equal to one another? Only if they are both equal to a constant…lets
call that constant
Of course, it’ll become obvious quickly that the separation
constant actually IS the total energy.
Separation constant

Page 3
Note that the beautiful separation only happened because the potential
and NOT
Now we have the time independent Schrodinger equation:
And it looks like the time dependence is really easy to solve:
The solution is:
O.k. so total solution is always
K.E. + P.E. = Total Energy
and we read that:
Hummm, more generally the soln is actually :
WAIT !!!!
What just happened here…why a sum? What are these c’s in front of Psi?
Lets do a
Total energy

Page 4
Warm-up question:
In the classically forbidden region for a finite potential well,
the physically meaningful solution to the Schrodinger
equation is
is always a real positive constant)
a. a cosine function (cos(x/
) )
b. the sum of sine and cosine functions
c. an increasing exponential
function( e
d. a decaying exponential
function( e
e. this question makes no sense
ans. d.
classically forbidden region,
E total less than potential energy V(x)

Page 5
one place where this model is “reasonably” accurate
Nanotechnology: how small does an object have to be
before movement of electrons starts to depend on size
and shape due to quantum effects?
Solving the Schrodinger equation for simple model
system (square well).
Easiest case of electron
confined to solve diff. equation.
Form of solutions
simpler, easier to understand basic ideas of QM.

Ace your assessments! Get Better Grades
Browse thousands of Study Materials & Solutions from your Favorite Schools
UBC Vancouver
Great resource for chem class. Had all the past labs and assignments
Leland P.
Santa Clara University
Introducing Study Plan
Using AI Tools to Help you understand and remember your course concepts better and faster than any other resource.
Find the best videos to learn every concept in that course from Youtube and Tiktok without searching.
Save All Relavent Videos & Materials and access anytime and anywhere
Prepare Smart and Guarantee better grades

Students also viewed documents