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For a particle on a sphere (3D rotor), discuss why one needs to introduce the quantum...
7. Any electron in an atom will be descoribed byd A. one 8. which quantum number...
7. Any electron in an atom will be descoribed byd A. one 8. which quantum number gives the electron's"spint" A. distinct quantum numbers D. four Efive B. two C three B. C.m D. m E. 7 9. Which quantum number gives the electron's "orbital orientation?" B. C. m A. n 10. Which quantum number gives the electron's "energy?" A. n 11. Which quantum number gives the electron's "orbital shape I type? A. n B. C. me D. m E. z...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harm...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
Problem 3: A free particle of mass m in one dimension is in the state Hbr...
Problem 3: A free particle of mass m in one dimension is in the state Hbr Ψ(z, t = 0) = Ae-ar with A, a and b real positive constants. a) Calculate A by normalizing v. b) Calculate the expectation values of position and momentum of the particle at t 0 c) Calculate the uncertainties ΔΧ and Δ1) for the position and momentum at t 0, Do they satisfy the Heisenberg relation? d) Find the wavefunction Ψ(x, t) at a...
a) and b) (a) The simplest quantum mechanical model for describing electrical conduction in a metal...
a) and b)
(a) The simplest quantum mechanical model for describing electrical conduction in a metal is the free electron gas in three dimensions. The density of states D(E) is given as: V 2m D(E)- 277 An estimate of the average electron energy can be obtained using the following expression: SEN(E)dE (E) - TH(E)DE where n(E)dE is the number of occupied electron states in an energy interval E to E + dE. Use a suitable expression for n(E) and introduce...
1. Quantum harmonic oscillator (a) Derive formula for standard deviation of position measurement ...
1. Quantum harmonic oscillator (a) Derive formula for standard deviation of position measurement on a particle prepared in the ground state of harmonic oscillator. The formula will depend on h, m andw (b) Estimate order of magnitude of the standard deviation in (a) for the LIGO mirror of mass 10 kg and w 1 Hz. (c) A coherent state lo) is defined to be the eigenstate of the lowering operator with eigenvalue a, i.e. à lo)a) Write la) as where...
How many orbitals have the following set of quantum numbers: n= 5,6 = 3, m, =-1?...
How many orbitals have the following set of quantum numbers: n= 5,6 = 3, m, =-1? Select one: a. 6 @ b. o d. 3 G. e. 7 How many values are there for the magnetic quantum number (M) when the value of the angular momentum quantum number() is 42 Select one: a. 4 b. 15 coll O d. 9 t oe.2 If a hydrogen atom in the excited n = 3 state relaxes to the ground state, what is...
Griffiths Introductory to Quantum Mechanics (3rd Edition): Problem 7.9 Problem 7.9 Consider a particle of mass...
Griffiths Introductory to Quantum Mechanics (3rd Edition):
Problem 7.9
Problem 7.9 Consider a particle of mass m that is free to move in a one- dimensional region of length L that closes on itself (for instance, a bea that slides frictionlessly on a circular wire of circumference L, as Problem 2.46) (a) Show that the stationary states can be written in the form 2π inx/L where n 0, t l, 2, , and the allowed energies are In Notice that-with...
Discuss why it is only possible to produce the odd harmonics in a system with one...
Discuss why it is only possible to produce the odd harmonics in a system with one open end and one closed end (pictures will help!). Write down the relation between An and L for the n 1, 3, 5, and 7 harmonics, and calculate the wavelength and frequency of the fundamental resonant mode for L 0.875 m and f 686 Hz. Then calculate the wave velocity of this oscillation. Pipe with one open and one closed end Only the odd...
Particle in a box Figure 1 is an illustration of the concept of a particle in...
Particle in a box Figure 1 is an illustration of the concept of a particle in a box. V=00 V=00 V=0 Figure 1. A representation of a particle in a box, where the potential energy, V, is zero between x = 0 and x = L and rises abruptly to infinity at the walls. The Schrödinger equation for a particle in a box reads t² d²u Y +V(x)y = Ey 2m dx2 + (1) where ħ=h/21 , y represents the...
A particle undergoes simple harmonic motion (SHM) in one dimension. The r coordinate of the particle...
A particle undergoes simple harmonic motion (SHM) in one dimension. The r coordinate of the particle as a function of time is r(t)Aco() where A is the called the amptde" and w is called the "angular frequency." The motion is periodic with a period T given by Many physical systems are described by simple harmonic motion. Later in this course we will see, for example, that SHM describes the motion of a particle attached to an ideal spring. (a) What...
7. Any electron in an atom will be descoribed byd A. one 8. which quantum number gives the electron's"spint" A. distinct quantum numbers D. four Efive B. two C three B. C.m D. m E. 7 9. Which quantum number gives the electron's "orbital orientation?" B. C. m A. n 10. Which quantum number gives the electron's "energy?" A. n 11. Which quantum number gives the electron's "orbital shape I type? A. n B. C. me D. m E. z...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
Problem 3: A free particle of mass m in one dimension is in the state Hbr Ψ(z, t = 0) = Ae-ar with A, a and b real positive constants. a) Calculate A by normalizing v. b) Calculate the expectation values of position and momentum of the particle at t 0 c) Calculate the uncertainties ΔΧ and Δ1) for the position and momentum at t 0, Do they satisfy the Heisenberg relation? d) Find the wavefunction Ψ(x, t) at a...
a) and b)
(a) The simplest quantum mechanical model for describing electrical conduction in a metal is the free electron gas in three dimensions. The density of states D(E) is given as: V 2m D(E)- 277 An estimate of the average electron energy can be obtained using the following expression: SEN(E)dE (E) - TH(E)DE where n(E)dE is the number of occupied electron states in an energy interval E to E + dE. Use a suitable expression for n(E) and introduce...
1. Quantum harmonic oscillator (a) Derive formula for standard deviation of position measurement on a particle prepared in the ground state of harmonic oscillator. The formula will depend on h, m andw (b) Estimate order of magnitude of the standard deviation in (a) for the LIGO mirror of mass 10 kg and w 1 Hz. (c) A coherent state lo) is defined to be the eigenstate of the lowering operator with eigenvalue a, i.e. à lo)a) Write la) as where...
How many orbitals have the following set of quantum numbers: n= 5,6 = 3, m, =-1? Select one: a. 6 @ b. o d. 3 G. e. 7 How many values are there for the magnetic quantum number (M) when the value of the angular momentum quantum number() is 42 Select one: a. 4 b. 15 coll O d. 9 t oe.2 If a hydrogen atom in the excited n = 3 state relaxes to the ground state, what is...
Griffiths Introductory to Quantum Mechanics (3rd Edition):
Problem 7.9
Problem 7.9 Consider a particle of mass m that is free to move in a one- dimensional region of length L that closes on itself (for instance, a bea that slides frictionlessly on a circular wire of circumference L, as Problem 2.46) (a) Show that the stationary states can be written in the form 2π inx/L where n 0, t l, 2, , and the allowed energies are In Notice that-with...
Discuss why it is only possible to produce the odd harmonics in a system with one open end and one closed end (pictures will help!). Write down the relation between An and L for the n 1, 3, 5, and 7 harmonics, and calculate the wavelength and frequency of the fundamental resonant mode for L 0.875 m and f 686 Hz. Then calculate the wave velocity of this oscillation. Pipe with one open and one closed end Only the odd...
Particle in a box Figure 1 is an illustration of the concept of a particle in a box. V=00 V=00 V=0 Figure 1. A representation of a particle in a box, where the potential energy, V, is zero between x = 0 and x = L and rises abruptly to infinity at the walls. The Schrödinger equation for a particle in a box reads t² d²u Y +V(x)y = Ey 2m dx2 + (1) where ħ=h/21 , y represents the...
A particle undergoes simple harmonic motion (SHM) in one dimension. The r coordinate of the particle as a function of time is r(t)Aco() where A is the called the amptde" and w is called the "angular frequency." The motion is periodic with a period T given by Many physical systems are described by simple harmonic motion. Later in this course we will see, for example, that SHM describes the motion of a particle attached to an ideal spring. (a) What...
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