Problem 10.1E: State the postulates of quantum mechanics introduced throughout the chapter in your own words. Problem 10.2E Problem 10.3E: State whether the following functions are acceptable wavefunctions over the range given. If they are... Problem 10.4E: State whether the following functions are acceptable wavefunctions over the range given. If they are... Problem 10.5E Problem 10.6E Problem 10.7E: Evaluate the operations in parts a, b, and f in the previous problem. Problem 10.8E: The following operators and functions are defined: A=x()B=sin()C=1()D=10()p=4x32x2q=0.5r=45xy2s=2x3... Problem 10.9E Problem 10.10E: Indicate which of these expressions yield eigenvalue equations, and if so indicate the eigenvalue. a... Problem 10.11E: Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue.... Problem 10.12E: Why is multiplying a function by a constant considered an eigenvalue equation? Problem 10.13E Problem 10.14E: Using the original definition of the momentum operator and the classical form of kinetic energy,... Problem 10.15E: Under what conditions would the operator described as multiplication by i the square root of 1 be... Problem 10.16E: A particle on a ring has a wavefunction =12eim where equals 0 to 2 and m is a constant. Evaluate... Problem 10.17E: Calculate the uncertainty in position, x, of a baseball having mass 250g moving at 160km/hr with an... Problem 10.18E: For an atom of mercury, an electron in the 1s shell has a velocity of about 58(0.58) of the speed of... Problem 10.19E: Classically, a hydrogen atom behaves as if it were 74pm across. What is the uncertainty in momentum,... Problem 10.20E: The largest known atom, francium, has an atomic diameter of 540pm. What is the uncertainty in... Problem 10.21E: How is the Bohr theory of the hydrogen atom inconsistent with the uncertainty principle? In fact, it... Problem 10.22E: Though not strictly equivalent, there is a similar uncertainty relationship between the observables... Problem 10.23E: The uncertainty principle is related to the order of the two operators operating on a wavefunction.... Problem 10.24E Problem 10.25E Problem 10.26E: For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the... Problem 10.27E Problem 10.28E: A particle on a ring has a wavefunction =eim, where =0to2 and m is a constant. a Normalize the... Problem 10.29E Problem 10.30E Problem 10.31E Problem 10.32E: Normalize the following wavefunctions over the range indicated. You may have to use the integral... Problem 10.33E Problem 10.34E Problem 10.35E: For an unbound or free particle having mass m in the complete absence of any potential energy that... Problem 10.36E Problem 10.37E Problem 10.38E Problem 10.39E: Evaluate the expression for the total energies for a particle having mass m and a wavefunction... Problem 10.40E Problem 10.41E: Verify that the following wavefunctions are indeed eigenfunctions of the Schrdinger equation, and... Problem 10.42E: In exercise 10.41a, the wavefunction is not normalized. Normalize the wavefunction and verify that... Problem 10.43E Problem 10.44E Problem 10.45E: Explain why n=0 is not allowed for a particle-in-a-box. Problem 10.46E Problem 10.47E Problem 10.48E Problem 10.49E: Carotenes are molecules with alternating CC and C=C bonds in which the electrons are delocalized... Problem 10.50E: The electronic spectrum of the molecule butadiene, CH2=CHCH=CH2, can be approximated using the one... Problem 10.51E Problem 10.52E Problem 10.53E: Show that the normalization constants for the general form of the wavefunction =sin(nx/a) are the... Problem 10.54E Problem 10.55E Problem 10.56E: An official baseball has a mass of 145g. a Assuming that a baseball in New Orleans Superdome width... Problem 10.57E: Is the uncertainty principle consistent with our description of the wavefunctions of the 1D... Problem 10.58E Problem 10.59E Problem 10.60E: Instead of x=0 to a, assume that the limits on the 1-D box were x=+(a/2) to (a/2). Derive acceptable... Problem 10.61E: In a plot of ||2, the maximum maxima in the plot is/are called the most probable positions. What... Problem 10.62E Problem 10.63E Problem 10.64E: The average value of radius in a circular system, r, is determined by the expression r=0r4r2dr. a... Problem 10.65E Problem 10.66E Problem 10.67E Problem 10.68E Problem 10.69E Problem 10.70E: Assume that for a particle on a ring the operator for the angular momentum, p, is i(/). What is the... Problem 10.71E: Mathematically, the uncertainty A in some observable A is given by A=A2A2. Use this formula to... Problem 10.72E Problem 10.73E Problem 10.74E: Verify that the wavefunctions in equation 10.20 satisfy the three-dimensional Schrdinger equation. Problem 10.75E: An electron is confined to a box of dimensions 2A3A5A. Determine the wavefunctions for the five... Problem 10.76E: a What is the ratio of energy levels having the same quantum numbers in a box that is 1nm1nm1nm and... Problem 10.77E: Consider a one-dimensional particle-in-a-box and a three-dimensional particle-in-a-box that have the... Problem 10.78E Problem 10.79E Problem 10.80E Problem 10.81E Problem 10.82E: What are x,y, and z for 111 of a 3-D particle-in-a-box? The operators for y and z are similar to the... Problem 10.83E Problem 10.84E Problem 10.85E Problem 10.86E Problem 10.87E Problem 10.88E Problem 10.89E: Substitute (x,t)=eiEt/(x) into the time-dependent Schrdinger equation and show that it does solve... Problem 10.90E: Write (x,t)=eiEt/(x) in terms of sine and cosine, using Eulers theorem: ei=cos+isin. What would a... Problem 10.91E Problem 10.92E Problem 10.93E Problem 10.95E format_list_bulleted