Problem 7.1CYU: Check Your Understanding If a=3+4i , what is the product a* a? Problem 7.2CYU: Check Your Understanding Suppose that a particle with energy E is moving along the x-axis and is in... Problem 7.3CYU: Check Your Understanding For the particle in the example, find the probability Of locating it 0 and... Problem 7.4CYU: Check Your Understanding A sodium atom nukes a transition from the first excited state the wound... Problem 7.5CYU: Check Your Understanding A particle With mass m is moving along the x-axis in a given by the... Problem 7.6CYU: Check Your Understanding Which of the following wave functions is valid wave-function solution for... Problem 7.7CYU: Check your Understanding (a) Consider an infinite square well with wall boundaries x=0 and x=L. What... Problem 7.8CYU: Check Your Understanding The vibrational frequency of the hydrogen iodide HI diatomic molecule is... Problem 7.9CYU: Check Your Understanding Find the expectation value of the position for a particle in the ground... Problem 7.10CYU: Check Your Understanding A proton with kinetic energy 1.00 eV is incident on a square potential... Problem 1CQ: What is the physical unit of a wave function, (x,t)? What is the physical unit of the square of this... Problem 2CQ: Can the magnitude of a wave function (*(x,t)(x,t)) be a negative number? Explain. Problem 3CQ: What kind of physical quamtity does a wave function of an electron represent? Problem 4CQ: What is the physical meaning of a wave function of a particle? Problem 5CQ: What is the meaning of the expression "expectation value?" Explain. Problem 6CQ: If the formalism of quantum mechanics is 'more exact' than that of classical mechanics, why don't we... Problem 7CQ: Can the de Broglie wavelength of a particle be known precisely? Can the position of a particle be... Problem 8CQ: Can we measure the energy of a free localized particle with complete precision? Problem 9CQ: Can we measure both the position and momentum of a particle with complete precision? Problem 10CQ: What is the difference between a wave function (x,y,z) and a wave function (x,y,z,t) for the same... Problem 11CQ: If a quantum particle is in a stationary state, does it mean that it does not move? Problem 12CQ: Explain the difference between time-dependent and independent SchrÖdinger's equations. Problem 13CQ: Suppose a wave function is discontinuous at some point. Can this function represent a quantum state... Problem 14CQ: Using the quantum particle in a box model, describe how the possible energies of the particle are... Problem 15CQ: Is it possible that when we measure the energy of a quantum particle in a box, the measurement may... Problem 16CQ: For a quantum panicle in a box, the first excited state (2) has zero value at the midpoint position... Problem 17CQ: Is it possible to measure energy of 0.75h for a quantum harmonic oscillator? Why? Why not? Explain. Problem 18CQ: Explain the connection between Planck's hypothesis of energy quanta and the energies of the quantum... Problem 19CQ: If a classical harmonic oscillator can at rest, why can the quantum harmonic oscillator never be at... Problem 20CQ: Use an example of a quantum particle in a box or a quantum oscillator to explain the physical... Problem 21CQ: Can we simultaneously measure position and energy of a quantum oscillator? Why? Why not? Problem 22CQ: When an electron and a proton of the same kinetic energy encounter a barrier of the same height and... Problem 23CQ: What decreases the tunneling probability most: doubling the barrier width or halving the kinetic... Problem 24CQ: Explain the difference between a box-potential and a of a quantum dot. Problem 25CQ: Can a quantum particle 'escape' from an infinite potential well like that in a box? Why? Why not? Problem 26CQ: A tunnel diode and a resonant-tunneling diode both utilize the same physics principle of quantum... Problem 27P: Compute |(x,t)|2 for the function (x,t)=(x)sint, where is a real constant. Problem 28P: Given the complex-valued function f(x,y)=(xiy)/(x+iy), calculate |f(x,y)|2. Problem 29P: Which one of the following functions, and why, qualifies to be a wave function of a particle that... Problem 30P: A particle with mass m moving along the x-axis and its quantum state is represented by the following... Problem 31P: A wave function of a particle with mass m is given by (x)={Acosax, 2ax+ 2a;0, otherwise where a... Problem 32P: A velocity measurement of an a-particle has been performed with a precision of 0.02 mm/s. What is... Problem 33P: A gas of helium atoms at 273 K is in a cubical container with 25.0 cm on a side. (a) What is the... Problem 34P: If the uncertainty in the y -component of a proton's position is 2.0 pm, find the minimum... Problem 35P: Some unstable elementary particle has a rest energy of 80.41 GeV and an uncertainty in rest energy... Problem 36P: An atom in a metastable state has a lifetime of 5.2 ms. Find the minimum uncertainty in the... Problem 37P: Measurements indicate that an atom remains in an excited state for an average time of 50.0 ns before... Problem 38P: Suppose an electron is confined to a region of length 0.1 nm (of the order of the size of a hydrogen... Problem 39P: Combine Equation 7.17 and Equation 7.18 to show k2=2c2. 2Ex2=1c22Et2 E(x,t)=Asin(kxt), Problem 40P: Show that (x,t)=Aei(kwt) is a valid solution to Schrödinger's time-dependent equation. Problem 41P: Show that (x,t)=Asin(kxt) and (x,t)=Acos(kxt) do not obey Schrödinger's time-dependent equation. Problem 42P: Show that when 1(x,t) and 2(x,t) are solutions to the time-dependent Schrödinger equation and A, B... Problem 43P: A particle with mass m is described by the following wave function: (x)=Acoskx+Bsinkx, where A, B,... Problem 44P: Find the expectation value of the kinetic energy for the particle in the state, (x,t)=Aei(kxt). What... Problem 45P: Find the expectation value of the square of the momentum squared for the particle in the state,... Problem 46P: A free proton has a wave function given by (x,t)=Aei(5.021011x8.001015t) . The coefficient of x is... Problem 47P: Assume that an electron in an atom can be treated as if it were confined to a box of width 2.0 A .... Problem 48P: Assume that a proton in a nucleus can be treated as if it were confined to a one-dimensional of... Problem 49P: An electron confined to a box has the ground state energy of 2.5 eV. What is the width of the box? Problem 50P: What is the ground state energy (in eV) of a proton confined to a one-dimensional box the size of... Problem 51P: What is the ground state energy (in eV) of an a -particle confined to a one-dimensional box the size... Problem 52P: To excite an election in a one-dimensional box from its first excited state to its third excited... Problem 53P: An electron confined to a box of width 0.15 nm by infinite potential energy barriers emits a photon... Problem 54P: If the energy of the first excited state of the electron in the box is 25.0 eV, what is the width of... Problem 55P: Suppose an electron confined to a emits photons. The longest wavelength that is registered is 500.0... Problem 56P: Hydrogen H2 molecules are kept at 300.0 K in a cubical container with a side length of 20.0 cm.... Problem 57P: An electron is confined to a box of width 0.25 nm. (a) Draw an energy-level diagram representing the... Problem 58P: An electron in a box is in the ground state with energy 2.0 eV. (a) Find the width of the box. (b)... Problem 59P: Show that the two lowest energy states of the simple harmonic oscillator, 0(x) and 1(x) from... Problem 60P: If the ground state energy of a simple harmonic oscillator is 1.25 eV, what is the frequency of its... Problem 61P: When a quantum harmonic oscillator makes a transition from the (n+1) state to the n state and emits... Problem 62P: Vibrations of the hydrogen molecule H2 can be modeled as a simple harmonic oscillator with the... Problem 63P: A particle with mass 0.030 kg oscillates back-and- forth on a spring with frequency 4.0 Hz. At the... Problem 64P: Find the expectation value x2 of the square of the position for a quantum harmonic oscillator in the... Problem 65P: Determine the expectation value of the potential energy for a quantum harmonic oscillator in the... Problem 66P: Verify that given by Equation 7.57 is a solution of Schrödinger's equation for the quantum harmonic... Problem 67P: Estimate the ground state energy of the quantum harmonic oscillator by Heisenberg's uncertainty... Problem 68P: A mass of 0.250 kg oscillates on a spring with the force constant 110 N/m. Calculate the ground... Problem 69P: Show that the wave function in (a) Equation 7.68 satisfies Equation 7.61, and (b) Equation 7.69... Problem 70P: A 6.0-eV electron impacts on a barrier with height 11.0 eV. Find the probability of the electron to... Problem 71P: A 5.0-eV electron impacts on a barrier of with 0.60 nm. Find the probability of the electron to... Problem 72P: A 12.0-eV electron encounters a barrier of height 15.0 eV. If the probability of the electron... Problem 73P: A quantum particle with initial kinetic energy 32.0 ev encounters a square barrier with height 41.0... Problem 74P: A simple model of a radioactive nuclear decay assumes that a-particles are trapped inside a well of... Problem 75P: A muon, a quantum particle with a mass approximately 2(X) times that of an electron, is incident on... Problem 76P: A grain of sand with mass 1.0 mg and kinetic energy 1.0 J is incident on a potential energy barrier... Problem 77AP: Show that if the uncertainty in the position of a particle is on the order of its de Broglie's... Problem 78AP: The mass of a -meson is measured to be 770MeV/c2 with an uncertainty of 100MeV/c2. Estimate the... Problem 79AP: A particle of mass m is confined to a box of width L. If the particle is in the first excited state,... Problem 80AP: A particle in a box [0; L] is in the third excited state. What are its most probable positions? Problem 81AP: A 0.20-kg billiard ball bounces back and forth without losing its energy between the cushions of a... Problem 82AP: Find the expectation value of the position squared when the particle in the box is in its third... Problem 83AP: Consider an infinite square well with wall boundaries x=0 and x=L. Show that the function (x)=Asinkx... Problem 84AP: Consider an infinite square well with wall boundaries x=0 and x=L. Explain why the function... Problem 85AP: Atoms in a crystal lattice vibrate in simple harmonic motion. Assuming a lattice atom has a mass of... Problem 86AP: A diatomic molecule behaves like a quantum harmonic oscillator with the force constant 12.0 N/m and... Problem 87AP: An electron with kinetic energy 2.0 MeV encounters a potential energy barrier of height 16.0 MeV and... Problem 88AP: A beam of mono-energetic protons with energy 2.0 MeV falls on a potential energy barrier of height... Problem 89CP: An electron in a long, organic molecule used in a dye laser behaves approximately like a quantum... Problem 90CP: In STM, an elevation of the tip above the surface being scanned can be determined with a great... Problem 91CP: If STM is to detect surface features with local heights of about 0.0200 nm, what percent change in... Problem 92CP: Use Heisenberg's uncertainty principle to estimate the ground state energy of a particle oscillating... Problem 93CP: Suppose an infinite square well extends from L/2 to +L/2 . Solve the time-independent Schrödinger's... 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... format_list_bulleted
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