Suppose a particle has a wavefunction image. Sketch the form of this wavefunction. Where is the particle most likely to be found? At what values of x is the probability of finding the particle reduced by 50 per cent from its maximum value?
I believe I understand the first two parts of the question, but I am confused on how to set up an equation to solve the last part. Please explain/show steps. Thanks!
Suppose a particle has a wavefunction image. Sketch the form of this wavefunction. Where is the...
If the particle has a wavefunction Psi(x) =Ne^(-ax2) Sketch the form of the wavefunction. Where is the particle most likely to be found? At what values of the x is the probability of finding a particle reduced by 50% from its maximum value.
2.2 Two-level system A particle in the box is described by the following wavefunction 1 1 V(x, t) + V2 V2 = Um(x)e -i(Em/h) In other words, this state is a superposition of two modes: n-th, and m-th. A superposition that involves only two modes (not necessarily particle in the box modes, but any two modes) is called a "two-level system”. A more modern name for such a superposition is a "qubit”. a) Come up with an expression for the...
Question #9 all parts thanks 9. The wavefunction, p(x,t), of a particle moving along the x-axis, whose potential energy V(x) is independent of time, is described by the one-dimensional non-relativistic Schrödinger equation (where m is its mass, h is the reduced Planck constant, i is the imaginary number): 2m (a) Verify that it is a parabolic equation (page E-1-2). [It has wave-like solutions, however.] (b) Use the substitution Px,t)-Xx)Tt) to separate the equation into two ODEs. (c) Solve for T,...
2.5 ty which will be discussed in chapter 4 2.3 Consider a particle of mass m subject to a one-dimensional potential V(x) that is given by V = 0, x <0; V = 0, 0<x<a; V = Vo, x> Show that bound (E < Vo) states of this system exist only if k cotka = -K where k2 = 2mE/12 and k' = 2m(Vo - E)/h4. 2.4 Show that if Vo = 974/2ma, only one bound state of the system...
4. (a) A particle in 1D has the wavefunction (x) = Ce-ex?12, where e > 0 and you may assume C > 0. i) Find the normalisation constant C. [4 marks] ii) For small e > 0, show that y is approximately a zero eigenvector of the momentum operator Ộ, i.e., show that lim lôy || = 0. €0+ Hint: for a > 0, recall that Se-ax?dx = Vola and Sox?e-ax?dx = Vra-312 [6 marks] (b) Let Ê be a...
I have a homework assignment for an Intro to Math Economics Class that I'm having difficulty understanding. (Short Run Phillips Curve Problem) A short-run Phillips curve for our purposes is simply the rate of inflation as a function of the rate of unemployment. Suppose that we have found that over the years that the Phillips curve had a very simple form, namely, that the product of the inflation rate and the unemployment rate was always 20 percent no matter what...
I just want to clarify what I need help on (as I do not need help on the full question). Specifically what I want is to be able to set the equations given to me so that I can solve for n using a root finding algorithm (which I already have). As I understand, I need something of the form | Tn(x) - e^x | = epsilon machine = (x^(n+1) / (n+1)!) and all I need from there is to...
Please be specific, thanks! (2) Why First-Order Systems (of a Specific Form) Are Sufficient: In class I stated that all systems of differential equations can be turned into first-order systems. And I wrote that first-order systems can be written in the form: For 3-by-3 system, the form is: r-f(r, y,z,t) y- g(x, y, z, t) , = h(z,y,z, This can be generalized to any number of unknown functions. a) Notice that r', y', and z are not included in the...
I need help in this problem but not with the physics part, I'm stuck with the algebra, the book skips some algebra steps and I'me getting stuck there, I need to understand how they eliminate K and q3, and also when they are solving for x, what happened to the other x, if you could do that part doing all the algebra steps I would appreciate it so much. Thanks Example 23.3 Where ls the Net Force Zero? AM Three...
Hello, I am trying to solve problem 15.1 which is shown in the first image. I attached extra images that explain what an arrow mean in the question and what the 4 dot symbol mean. The RT1 is the separation axiom 1. I also attached what is meant by a discrete and indiscrete space. The last image give the answer from the book, but I need an explanation. this problem is from "Elementary topology problem textbook". Please have clear hand...