Model 2 The following are the normalized solutions to the Schrödinger equations for a particle confined...
Model 2 The following are the normalized solutions to the Schrödinger equations for a particle confined to a plane defined in Model 1. n joc inn ny -sin- ab nh² nh² E, (x,y)=- +- 8ma? 8mb? The contour plots below represent three different wavefunctions for a system such that a = b corresponding to the length of the horizontal x axis and vertical y axis, respectively. b- (iii) 12. Identify the values of the quantum numbers n, and n, for...
8. Compare the expression derived for translational energy for a particle confined to a 2D plane, Em..., to one confined to a 1D line, E, or E. Does there appear to be a general relationship between the two solutions? If so, specifically identify how they are related. Model 2 The following are the normalized solutions to the Schrödinger equations for a particle confined to a plane defined in Model 1. V.,„, (x,y)= \sin ",7 sin ", Ty E. (x,y) =...
7. Compare the functional form of the wavefunction derived for a particle confined to a 2D plane, Y., , to one confined to a 1D line, Y., or Y... Does there appear to be a general relationship between the two solutions? If so, specifically identify how they are related. Model 2 The following are the normalized solutions to the Schrödinger equations for a particle confined to a plane defined in Model 1. V., ,(x,y) = Pnevy »* Vaba sin2= sin2,...
(15) 4. The state of the particle-in-a box located between 0<x<a is described by the following normalized wavefunction at t=0: Y(x,t=0) =(1/2) A Sin (fx/a)-(1/12) A Sin(3 rex/a) + (1/2) A Sin(5tx/a) (10) a) If the energy of the system is measured at t=0, what energies will be observed What is the probability (in percent) of observing an energy E> 9h-/8ma?? on
1 Particle in a Box with a Bump (based on B&J 4.11) Consider a particle of mass m in a 1-D double well with potential given by Vo, 05\x\<b V(x) = { 0, b<\x<c 100, [x]>c . We will study the lowest energy states, for which 0 <E<V, corresponding to tunnelling between the two wells. (a) Write down the time-independent Schödinger equation in the three regions -c<x<-b, –b< <b, and b< I< c. Write down the most general wavefunction solution...
please solve number 2 and number 4 from the following picture. 2. The equivalent s-domain model for an RC circuit is shown below. w The loop equation in the s-domain is given by: 3165) + 16 = 3244 Determine the current i(t). Use the phase shift approach. 3. Determine the inverse Laplace transform of s? Y(s) - 10s +3[sY(s) - 10 ] + 2Y(s) = - 4. Clearly answer the following questions: a. Explain the purpose of using the Laplace...