For a solution to be a physical solution, it must satisfy several criteria. First, it must be continuous everywhere. Second, it must have a continuous derivative everywhere, except for points where the potential energy becomes infinite (as it does at the walls of the box). Finally, it must be normalizable.
In this case, you can check the first criterion by noting that the two functions Csin(nπx/L) and 0 are continuous and that they have the same value at x=0 and x=L, where their domains meet. To check the second criterion, simply take the first derivative of Csin(nπx/L) and 0. Both derivatives are continuous functions in their domains. The points where the domains meet are exactly the points where the potential energy becomes infinite, so you don't have to check for continuity there. The third criterion requires that there exist some value of C such that:
[infinity]
∫ |ψ(x)|^2. dx=1
-[infinity]
Since ψ(x) is zero outside the interval 0<=x <=L, this equation reduces to
L
∫ C^2 sin^2(nπx/L)dx=1
0
Use this equation to find the unique positive value of C.
Express your answer in terms of L.
Answers: 2
Physics, 22.06.2019 10:20, studyowl9192
Electromagnetic induction. a coil of wire contains n turns and has an electrical resistance r. the radius of each turn is a. initially, inside the coil there exists a uniform magnetic field of magnitude b0 parallel to the axis of the coil. the magnetic field is then reduced slowly. the current induced in the coil is i. how long does it take for the magnitude of the uniform field to drop to zero?
Answers: 1
Physics, 22.06.2019 18:30, raywalker3410
Adisk with a radius of r is oriented with its normal unit vector at an angle q with respect to a uniform electric field. which of the following would result in an increase in the electric flux through the disk? check all that apply? a. increasing the area of the disk b. decreasing the given orientation angle of the disk c. decreasing the strength of the electric field d. increasing the given orientation angle of the disk, but not exceeding an angle of 90
Answers: 1
For a solution to be a physical solution, it must satisfy several criteria. First, it must be contin...
Mathematics, 19.05.2020 18:09
English, 19.05.2020 18:09
Mathematics, 19.05.2020 18:09
History, 19.05.2020 18:09
Mathematics, 19.05.2020 18:09