4 QUESTION 1Consider a system with Hamiltonian operator Â that is in a state wk with energy Ex, whereand k is the quantum number. The function Uk is normalized, and it is also an eigenfunction of an operator n with eigenvalue w:合= uゆWhich one of the following statements is incorrect?Oa câ> - wkOb.cô> = wO.it is not possible to measure the observable property 2 with zero uncertainty.= 0

For ΩΛψk =Wkψk (eigen value equation). Now, the average value of the parameter associated with the…

Consider a system with Hamiltonian operator A that is in a state , with energy Ex. where and k is the quantum number. The function , is normalized, and it is also an eigenfunction of an operator î with eigenvalue w Which one of the following statements is incorrect? Oc t is not possible to measure the observable property 2 with zero uncertainty. Oecf> =

Consider a system with Hamiltonian operator A that is in a state , with energy Ex. where and k is the quantum number. The function , is normalized, and it is also an eigenfunction of an operator î with eigenvalue w Which one of the following statements is incorrect? Oc t is not possible to measure the observable property 2 with zero uncertainty. Oecf> =

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter4: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 37P: (a) Using Equation 4.36, make a graph of the n=3 wave function and the square of this wave function...

See similar textbooks

Similar questions

What is the eigenvalue for the eigenfunction e^(-2√3) ?
(a) Using Equation 4.36, make a graph of the n=3 wave function and the square of this wave function for a particle in a box with the edges at x=0 and x=7 . Estimate the probability of finding the particle between x1=3 and x2=4 . You may either do an integral or find the area under the curve by counting the number of rectangular boxes (roughly estimating the fractional boxes), and then multiply by the area of each box, watching your units. Show your calculation with units for credit. (b) Verify that the n=3 wave function in (a) is an allowed quantum state (sometimes called an eigenfunction) of by substituting it for in the left side of the equation =E immediately following Eq. 4.32. Calculate the derivatives to see if your result E is a constant multiplied by the original n=3 wavefunction. What does the constant you get tell you about the energy of thiseigenstate? Is it in agreement with the energy for the n=3 level you would calculate from Equation 4.37?
A particle of mass m is placed in a three-dimensional rectangular box with edge lengths 2L, L, and L. Inside the box the potential energy is zero, and outside it is infinite; therefore, the wave function goes smoothly to zero at the sides of the box. Calculate the energies and give the quantum numbers of the ground state and the first five excited states (or sets of states of equal energy) for the particle in the box.
Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue. a ddxcos4xb d2dx2cos4x c px(sin2x3)d x(2asin2xa) e 3(4lnx2), where 3=3f ddsincos g d2d2sincosh ddtan
Indicate which of these expressions yield eigenvalue equations, and if so indicate the eigenvalue. a ddxsinx2b d2dx2sinx2 c iddxsinx2d iddxeimx, where m is a constant e ddx(ex)f (22md2dx2+0.5)sin2x3 g ddy(ey2)
The speed of a certain proton is 0.45 Mm s−1. If the uncertainty in its momentum is to be reduced to 0.0100 per cent, what uncertainty in its location must be tolerated?
How many orbit of are at their in the 3rd shell (n=3)?
How many distinct sets of all 4 quantum numbers are there with n = 4 and ml = -2? (I got 10 is that correct?)
Question 1 Which of the following functions are Eigen functions of the operator d2/dx2 a) y (x) = x4 b) y (x) = cos3x
Suppose a particle of mass m is in a reg ion where its potential energy varies as aX4, where a is a constant. Write down the corresponding Schr6dinger equation.
How many eigenstates of a 3D particle in a box have eigenvalue of E=38h2/(8ma2) if a=b=c? Would changing c change this number?
Which of the following functions can be normalized (in all cases the range for x is from x= (-infinity) to (infinity), and a is a positive constant): (i) sin(ax); (ii) cos(ax)e-x^2? Which of these functions are acceptable as wavefunctions? Source: Atkins Physical Chemistry 11th Edition, E7B.4(b)