None H.W.4Q. A particle is moving in one-dimension that characterized by the state (w) with wave function yr=Aewhere qis a real constant.(a) Determine A(b) Calculate the uncertainty of position AxNote: you can use the integral form fx*e"dr =n= Q1,2..

Given:- A particle is moving in one -dimension that is characterized by the state ψ with the wave…

Answered: Q. Aparticle is moving in one-dimension…

Q. Aparticle is moving in one-dimension that characterized by the state Iw) with wave function y-Ae where q is a real constant. (a) Determine A (0 Calulate the uncertainty of nosition Ar

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter7: Quantum Mechanics

Section: Chapter Questions

Problem 94CP: A particle of mass m confined to a box of width L is in its first excited state 2(x). (a) Find its...

See similar textbooks

Similar questions

At time t = 0 the wave function for a particle in a box is given by the function in the provided image, where ψ1(x) and ψ1(x) are the ground-state and first-excited-state wave functions with corresponding energies E1 and E2, respectively. What is ψ(x, t)? What is the probability that a measurement of the energy yields the value E1? What is <E>?
A particle of mass m is confined to a box of width L. If the particle is in the first excited state, what are the probabilities of finding the particle in a region of width0.020 L around the given point x: (a) x=0.25L; (b) x=040L; (c) 0.75L and (d) x=0.90L.
If the position of an electron in a membrane is measured to an accuracy of 3.58 µm, what is the electron's minimum uncertainty in velocity (in m/s)? a) If the electron has this velocity, what is its kinetic energy in eV? b) What are the implications of this energy, comparing it to typical molecular binding energies?
A 0.500kg block rests on the frictionless, icy surface of a frozen pond . if the location of the block is measured to a precision of 0.150 cm and its mass known exactly,what is the minimum uncertainty in the block's speed?
An electron is bound in a square well of width 1.05 nm and depth U0=6E∞, where E∞ is the ground-state energy for an infinitely deep potential well.If the electron is initially in the ground level, E1=0.625E∞ , and absorbs a photon, what maximum wavelength can the photon have and still liberate the electron from the well?
A one-dimensional infinite well of length 200 pm contains an electron in its third excited state.We position an electrondetector probe of width 2.00 pm so that it is centered on a point of maximum probability density. (a) What is the probability of detection by the probe? (b) If we insert the probe as described 1000 times, how many times should we expect the electron to materialize on the end of the probe (and thus be detected)?
What is the independent wave function for a particle in a box x=0,L
Consider the wave function phi(x) = A sin(kx) where k = 2pi/lambda and A is a real constant. (a) What are the values of x that have the highest probability of finding the particle described by this wave function? (b) What are the values of x that have zero probability of finding the particle described by this wave function?
The wavefunction for a quantum particle tunnelling through a potential barrier of thickness L has the form ψ(x) = Ae−Cx in the classically forbidden region where A is a constant and C is given by C^2 = 2m(U − E) /h_bar^2 . (a) Show that this wavefunction is a solution to Schrodinger’s Equation. (b) Why is the probability of tunneling through the barrier proportional to e ^−2CL?
What is the smallest box in which you can confine an electron if you want to know for certain that the uncertainty in the electron’s speed is no more than 20 m/s?
An electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV and L = 950 pm as shown in Figure P40.21. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero.(b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.50-eV electron tunneling through the barrierto be one in one million?
A one-dimensional harmonic oscillator wave function is ψ = Axe-bx2(a) Show that ψ satisfies as shown. (b) Find b and the total energy E. (c) Is this wave function for the ground state or for the first excited state?