Physics, 24.08.2019 00:30 flowerrbabie
Consider the infinite spherical well of radius a. in lecture we found that the solution to the radial equation was u(r) = ar je(kr). in this problem we will consider the solutions when l = 1. (a) extra part (not for credit) show that j1(x) = sinc cosc c22 2 - using the definition j(x) = (-2)* () (sinu). (b) extra part (not for credit) find and sketch the effective potential veff. e(r) for l = 1 and explicitly check that ur) = arji(kr) solves the one-dimensional tise for this potential. let me be the n-th zeros or roots of the l-th spherical bessel functions so that bu is the first zero of j1(2), b21 is the second zero of ji(2), etc. just as we did with the one-dimensional finite square well, we can use graphical methods to find these roots and thus the allowed energies. (c) show that j1(x) = 0 implies x = tanx. plot x and tanx on the same graph and locate the points of intersection (the x values of these intersection points gives us our bessel function zeros bni). note that x = 0) and thus e= 0 is a solution. even though x = 0 solves x = tan z we don't use it to give us a physically allowed energy. why not? [note: your graph doesn't have to be too fancy. you can just make a sketch, you don't need to use a grapher or print anything out. nor do you do need to numerically solve for the roots in this part.) (d) argue from your graphical solution that, for large n, the energies satisfy h272 eni ~ m2 (n + ). (1) (e) using whatever method you'd like, find the energies en,1 for n=1 and n = 5. express these energy as a number times h272 /2ma? . f) going back to the full 3d problem, what is the degeneracy of the n = 1, 1 = 1 state? write out the full wave function 0110(r, 0,0) explicitly (the indices on y mean n = 1, 1 = 1, and m = 0).2 you do not have to solve for the normalization constant.
Answers: 3
Physics, 22.06.2019 05:30
Astudent pushes on a 20.0 kg box with a force of 50 n at an angle of 30° below the horizontal. the box accelerates at a rate of 0.5 m/s2 across a horizontal floor. what is the value of the normal force on the box? 200 n 243 n 156 n 225 n
Answers: 2
Physics, 22.06.2019 09:00
When a bicycle coasts uphill, it moves slower and slower as it climbs. why? a. its kinetic energy is transforming into heat energy. b. its potential energy is transforming into kinetic energy. c. its kinetic energy is transforming into potential energy and heat energy. d. its potential energy is transforming into kinetic energy and heat energy.
Answers: 1
Physics, 22.06.2019 14:20
Antireflective coatings on solar cells are often made by applying a thin film of silicon nitride (sinx), which has an index of refractive of 1.2, on the top of the silicon solar cell, which has a refractive index of about 3.5. however, the sun emits radiation of various wavelengths which the solar cell absorbs, and the antireflective coating can only absolutely minimize the reflection of one of these wavelengths. the coating thickness is chosen to reduce the reflection of green/yellow light (e = 2.2 ev), which is the most intense color in the solar spectrum (shown below). which of the following coatings would minimize reflection of green/yellow light? the answer is 820 nm how? what is the angular width of the central maximum of an electron traveling at 2 x 108 m/s going through a single slit of width 1 mm.
Answers: 1
Consider the infinite spherical well of radius a. in lecture we found that the solution to the radia...
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