A free particle moving in one dimension has wave function
Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)]
where k and ω are positive real constants.
At t = π/(6ω) what are the two smallest positive values of x for which the probability function |Ψ(x,t)|2 is a maximum? Express your answer in terms of k.
A free particle moving in one dimension has wave function Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)] where k and ω are...
Consider a wave that is represented by ψ(x, t) = 4 cos (kx − ωt). where k = 2π/λ and ω = 2πf. The aim of the following exercises is to show that this expression captures many of the intuitive features of waves. a) Consider a snapshot of the wave at t = 0. Use the expression to find the possible values of x at which the crests (maximum points) of the wave are located. By what distance are neighboring...
5. A free particle has the initial wave function, where A and a are positive real constants. (a) Normalize ψ(x,0). (b) Find φ(k). (c) Construct $(z,t), in the forn of an integral. (d) Discuss the limiting cases (a very large, and a very small).
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0, otherwise where a and A are positive real numbers. The particle is in a zero (or constant) potential environment since it is a free particle a) Determine A from normalization. b) Determine φ(p) = Φ(p,0), the time-zero momentum representation of the particle state. What is Φ(p,t)? Sketch φ(p). Locate the global maximum and the zeros of φ(p). Give the expression for the zeros (i.e.,...
A free proton has a wave function Psi (x) = A sin (kx), where k = 1.2 times 10^10 m^-1 What is the proton's lambda? What is the proton's momentum? What is the proton's speed? Normalize Psi (x) if the wave only exists inside an infinite square well with width a = 2.1 m, (so that Psi (x) = A sin (kx) between 0 < x < a and Psi (x) = 0 otherwise).
Consider a particle confined to one dimension and positive with the wave function Nxear, x20 x<0 0 where N is a real normalization constant and α is a real positive constant with units of (length)-1. For the following, express your answers in terms of α: a) Find the normalization constant N. What are the units of your result and do they make sense? b) What is the most probable location to find the particle, or more precisely, at what z...
9. 1.66 points Show that the wave function ψ-A ei(kx-at) is a solution to the Schrödinger equation, given below, where k-2π / λ and U-0. 2m dz2 Accomplish by calculating the following quantities. (Use the following as necessary: A, K, x, ,t, h, and m.) momentum Need Help?Read ItTalk to a Tutor 9. 1.66 points Show that the wave function ψ-A ei(kx-at) is a solution to the Schrödinger equation, given below, where k-2π / λ and U-0. 2m dz2 Accomplish...
A particle moving in one dimension is described by the wave function$$ \psi(x)=\left\{\begin{array}{ll} A e^{-\alpha x}, & x \geq 0 \\ B e^{\alpha x}, & x<0 \end{array}\right. $$where \(\alpha=4.00 \mathrm{~m}^{-1}\). (a) Determine the constants \(A\) and \(B\) so that the wave function is continuous and normalized. (b) Calculate the probability of finding the particle in each of the following regions: (i) within \(0.10 \mathrm{~m}\) of the origin, (ii) on the left side of the origin.
1. A free particle of mass m moving from the left in one dimension scatters from the potential V(x) αδ(x). Suppose that the wave number of the particle is k and that α > 0. a. State the general form of the wave function including reflected and transmitted waves. b. Find the amplitude t of the transmitted wave in terms of α, k, m, and h. Find T
A free electron has a wave function ψ(x)= Asin (5x1010 x) where x is measured in meters. Find the electron's de Broglie wavelength the electron's momentum a. b, 3. When an electron is confined in the semi-infinite square, its wave function will be in the form Asin kx for0<x<L ψ(x)- Ce for x> L having L = 5 nm and k = 1.7 / nm. a. Find the energy of the state. b. Write down the matching conditions that the...
Consider a particle confined to one dimension and positive r with the wave function 0, z<0 where N is a real normalization constant and o is a real positive constant with units of (length)-1. For the following, express your answers in terms of a: a) Calculate the momentum space wave function. b) Verify that the momentum space wave function is normalized such that (2.4) c) Use the momentum space wave function to calculate the expectation value (p) via (2.5)