1 The Nature Of Light 2 Geometric Optics And Image Formation 3 Interference 4 Diffraction 5 Relativity 6 Photons And Matter Waves 7 Quantum Mechanics 8 Atomic Structure 9 Condensed Matter Physics 10 Nuclear Physics 11 Particle Physics And Cosmology Chapter7: Quantum Mechanics
Chapter Questions Section: Chapter Questions
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... Problem 6CQ: If the formalism of quantum mechanics is 'more exact' than that of classical mechanics, why don't we...
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Quantum mechanics
Why is the angular momentum quantized?!
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Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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