![3. /15 pts] Imagine solving the SE for a particular potential well and finding two stationary solutions. The first solution i](http://img.homeworklib.com/images/07c4373e-fa7f-4acb-a2e2-fc7101928d40.png?x-oss-process=image/resize,w_560)
Consider the quantum state ψ(r state at t = 0 is shown below: t)-V1 (a , t) + 2( , t A crude sketch of the PDF for this t 0 Figure 1: PDF at t 0. (a) Write an explicit time dependent form for Ψ(a,t) in terms of E0 (b) Sketch the PDF at time - Th/(2Fo). (c) Find an expression for the earliest time where the PDF is an even function (i.e., PDF (r)-PDF(-)). And sketch the PDF at this time.
Homework Answers
![+ 2x2-2Y2x) Exp[-x2], {x,-4, 4), AxesLabel Plot 2 EO PDF 2 EO 0.3 0.2 0.1 ()E], (x, -4, 4), axesLabel 4 EO PDF 0.35 0.25 0.20](http://img.homeworklib.com/images/4c6e7225-f880-44cb-95ca-a30f822959f7.png?x-oss-process=image/resize,w_560)
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3. /15 pts] Imagine solving the SE for a particular potential well and finding two stationary sol...
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 regio...
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 region 1 region 2 region 3 Figure 1: Semi-infinite potential for Problem 3 This potential is piecewise defined as follows where Uo is some positive value of energy. The three intervals in x have been labeled region 1,2 and 3 in Figure 1 Consider a particle of mass m f 0 moving in...
Can we find this without use of the moment generating function? 3. (15 pts) Let Xị...
Can we find this without use of the moment
generating function?
3. (15 pts) Let Xị and X2 be two independent random variables that follow standard normal distribution. The PDF of a standard normal distribution is given by f(t)= exp-/2; - <t<0.. i) Find the joint PDF of V = X1 + X2 and Y2 = X1 - X). ii) Prove that Yi and Y2 are independent. R ONALEN SON
2. Goal of this problem is to study how tunnelling in a two-well system emerges. In particular, w...
2. Goal of this problem is to study how tunnelling in a two-well system emerges. In particular, we are interested in determining how the tunnelling rate T' of a particle with mass m scales as a function of the (effective) height Vo - E and width b of an energy barrier separating the two wells. The following graphics illustrates the set-up. Initially the particle may be trapped on the left side corresponding to the state |L〉, we are now interested...
4) A particle in an infinite square well 0 for 0
4) A particle in an infinite square well 0 for 0
please help me solve part (c). 2,U2 1, x2 = 2 and yo = 0,31 0 3. Given the data x0 y for the polyno- a) (15 pts) Set up the Vandermonde system Vc mial interpolant p(x) = co + C1x + c2x2 such that...
please help me solve part (c).
2,U2 1, x2 = 2 and yo = 0,31 0 3. Given the data x0 y for the polyno- a) (15 pts) Set up the Vandermonde system Vc mial interpolant p(x) = co + C1x + c2x2 such that p(zi) = yi, 2 0,1,2 b) (15 pts) Find the solution of the system and sketch y px) c) (15 pts) Write down the Lagrange form of the interpolating poly- nomial and simplify the result....
A NON stationary state A particle of mass m is in an infinite square well potential of width L, a...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
The Finite Square Wel A more realistic version of the infinite square well potential has a...
The Finite Square Wel A more realistic version of the infinite square well potential has a finite well depth: -a V(x)--V for -a<x <a for x <-a,'r > a =0 This assignment will consider the bound states of a particle (of mass m) in this potential (i.e. total energy E <0). (1) Determine the general solutions to the time-independent Schrödinger equation for the three regions x <-a, -a<x <a, and > a. Write these solutions in terms of k and...
Please help! I need help finding and solving equations of equilibrium to find the max tension in ...
please help! I need help finding and solving equations of
equilibrium to find the max tension in the cables and the angle
that results in the maximum tension, I also have pictures below of
the work I have so far all I really need is equations for the 4
cable part and that's it but I put the whole assignment so you
could see thanks!
Tower Support System Challenge Challenge Scenario: Due to weather conditions, a major communication tower n...
specifically on finite i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at le...
specifically on finite
i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at least one xpeated digin? I. This is the oounting problem Al ancmher so ask yourelr (1) ls onder ipo n How many strings of four bexadeci ) A Compuir Science indtructor has a stack of blue can this i For parts c, d. and e, suppose...
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 region 1 region 2 region 3 Figure 1: Semi-infinite potential for Problem 3 This potential is piecewise defined as follows where Uo is some positive value of energy. The three intervals in x have been labeled region 1,2 and 3 in Figure 1 Consider a particle of mass m f 0 moving in...
Can we find this without use of the moment
generating function?
3. (15 pts) Let Xị and X2 be two independent random variables that follow standard normal distribution. The PDF of a standard normal distribution is given by f(t)= exp-/2; - <t<0.. i) Find the joint PDF of V = X1 + X2 and Y2 = X1 - X). ii) Prove that Yi and Y2 are independent. R ONALEN SON
2. Goal of this problem is to study how tunnelling in a two-well system emerges. In particular, we are interested in determining how the tunnelling rate T' of a particle with mass m scales as a function of the (effective) height Vo - E and width b of an energy barrier separating the two wells. The following graphics illustrates the set-up. Initially the particle may be trapped on the left side corresponding to the state |L〉, we are now interested...
4) A particle in an infinite square well 0 for 0
please help me solve part (c).
2,U2 1, x2 = 2 and yo = 0,31 0 3. Given the data x0 y for the polyno- a) (15 pts) Set up the Vandermonde system Vc mial interpolant p(x) = co + C1x + c2x2 such that p(zi) = yi, 2 0,1,2 b) (15 pts) Find the solution of the system and sketch y px) c) (15 pts) Write down the Lagrange form of the interpolating poly- nomial and simplify the result....
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
The Finite Square Wel A more realistic version of the infinite square well potential has a finite well depth: -a V(x)--V for -a<x <a for x <-a,'r > a =0 This assignment will consider the bound states of a particle (of mass m) in this potential (i.e. total energy E <0). (1) Determine the general solutions to the time-independent Schrödinger equation for the three regions x <-a, -a<x <a, and > a. Write these solutions in terms of k and...
please help! I need help finding and solving equations of
equilibrium to find the max tension in the cables and the angle
that results in the maximum tension, I also have pictures below of
the work I have so far all I really need is equations for the 4
cable part and that's it but I put the whole assignment so you
could see thanks!
Tower Support System Challenge Challenge Scenario: Due to weather conditions, a major communication tower n...
specifically on finite
i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at least one xpeated digin? I. This is the oounting problem Al ancmher so ask yourelr (1) ls onder ipo n How many strings of four bexadeci ) A Compuir Science indtructor has a stack of blue can this i For parts c, d. and e, suppose...
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