![6. The energy levels of a harmonic oscillator with angular frequency w are given by 2 (a) Suppose that a system of N almost independent oscillators has total energy E^Nhw 2 Mhw. Show that the number of states with exactly this energy equals the number of ways of distributing M identical objects among N compartments and that this number 1S MI(N 1) Hint: Consider the number of distinct arrangements of a set of M objects and N -1 partitions (b) Suppose that δΕ is very small compared with E but large compared with it. Write down an expression for 2(E), the number of states with energy between E and E +SE Hint: Assume that the number calculated in part (a) doesnt change appreciably in the small range between E and E + SE.] (c) Use Stirlings approximation to show that when N » 1 and M» 1, If N is of the order of Avogadros number, can you ignore the last term? (d) Show that when M N, the above result leads to a dependence of In Ω on E, which is compatible with the general result in Ω ~ fin(B)-const., where f is the number of degrees of freedom of the system (here f-N) and const. is independent of hE](http://img.homeworklib.com/questions/161690c0-7065-11ea-be11-25f24af92c90.png?x-oss-process=image/resize,w_560)
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6. The energy levels of a harmonic oscillator with angular frequency w are given by 2...
1. The energy levels of a quantum harmonic oscillator are given by E Planck constant, w...
1. The energy levels of a quantum harmonic oscillator are given by E Planck constant, w is the frequency of oscillation and n-0,1,2, Determine the following: (a) Show that the one-particle partition function is given by 211-exp-Bhu) oan 1 (1 Hint you will need to use the following formula for a geometric progression: (b) Show that the internal energy is given by (c) Show that the Helmoltz free energy is given by 1 In(1 exp Bha) (d) Show that the...
question no 4.22, statistical physics by Reif Volume 5 4.92 Mean energy of a harmonic oscillator A harmonic oscillator...
question no 4.22, statistical physics by Reif Volume 5
4.92 Mean energy of a harmonic oscillator A harmonic oscillator has a mass and spring constant which are such that its classical angular frequency of oscllation is equal to w. In a quantum- mechanical description, such an oscillator is characterized by a set of discrete states having energies En given by The quantum number n which labels these states can here assume all the integral values A particular instance of a...
Show that the energy of a simple harmonic oscillator in the n = 2 state is...
Show that the energy of a simple harmonic oscillator in the n = 2 state is 5ℏω/2 by substituting the wave functionψ2 = A(2αx2- 1)e-αx2/2 directly into the Schroedinger equation, as broken down in the following steps. First, calculate dψ2/dx, using A, x, and α. dψ2/dx = .......................... Second, calculate d2ψ2/dx2, using A, x, and α. d2ψ2/dx2 = ......................... Third, calculate α2x2ψ2 - d2ψ2/dx2, using A, x, and α. α2x2ψ2 - d2ψ2/dx2 = ....................... Fourth, calculate (α2x2ψ2 - d2ψ2/dx2)/ψ2, using...
Quantum, 1D harmonic oscillator. Please answer in full. Thanks. Q3. The energy levels of the 1D harmonic oscillator are given by: En = (n +2)ha, n=0. 1, 2, 3, The CO molecule has a (reduced) mass of...
Quantum, 1D harmonic oscillator. Please answer in full.
Thanks.
Q3. The energy levels of the 1D harmonic oscillator are given by: En = (n +2)ha, n=0. 1, 2, 3, The CO molecule has a (reduced) mass of mco = 1.139 × 10-26 kg. Assuming a force constant of kco 1860 N/m, what is: a) The angular frequency, w, of the ground state CO bond vibration? b) The energy separation between the ground and first excited vibrational states? 7 marks] The...
1. An ideal (frictionless) simple harmonic oscillator is set into motion by releasing it from rest...
1. An ideal (frictionless) simple harmonic oscillator is set into motion by releasing it from rest at X +0.750 m. The oscillator is set into motion once again from x=+0.750 m, except the oscillator now experiences a retarding force that is linear with respect to velocity. As a result, the oscillator does not return to its original starting position, but instead reaches = +0.700 m after one period. a. During the first full oscillation of motion, determine the fraction of...
4. (a) The energy states of Landau levels are given by where wc is the cyclotron frequency Using ...
4. (a) The energy states of Landau levels are given by where wc is the cyclotron frequency Using this and the 2D density of states given by where m is the carrier effective mass, deduce the degeneracy of a Landau Level Sketch these Landau levels on a graph of number n(E) verses energy (E), and indicate the position of the Fermi Energy for a filling factor of 8 4 (b) Sketch the band diagram for a heterojunction between p-type AlGaAs...
(30) Given the equilibrium bond length of CO is 1.138, explore population fractions (Eq. 2) of...
(30) Given the equilibrium bond length of CO is 1.138, explore population fractions (Eq. 2) of the ground state and first 15 pure rotational excited states relative to the ground state (where {=0). Mathematica is recommended. Do this at 298 K and at 100 K. Comment on how the results differ compared to part a). 1) In the application of quantum mechanical and statistical mechanical principles to samples containing large numbers of species (e.g. macroscopic samples of molecules), there is...
can you explaination for thes questions how did we got these right answers. Thankyou! w many photons of light with frequency 5.50 x 1015 Hz are required to provide 1 kJ of energy? 3364 x 10-18 2....
can you explaination for thes questions how did we got these
right answers. Thankyou!
w many photons of light with frequency 5.50 x 1015 Hz are required to provide 1 kJ of energy? 3364 x 10-18 2. What is the wavelength of a bullet that is 0.450 g traveling at 2000. m/s? A) 2000 nm B) 2.74 x 1020 C) 4.56 x 10 D) 1.65x 10 E)3.84x 10 B) 2/94 x 10-24 m C) 7.36 x 104 m D) 7.36...
1 Particle in a Box with a Bump (based on B&J 4.11) Consider a particle of...
1 Particle in a Box with a Bump (based on B&J 4.11) Consider a particle of mass m in a 1-D double well with potential given by Vo, 05\x\<b V(x) = { 0, b<\x<c 100, [x]>c . We will study the lowest energy states, for which 0 <E<V, corresponding to tunnelling between the two wells. (a) Write down the time-independent Schödinger equation in the three regions -c<x<-b, –b< <b, and b< I< c. Write down the most general wavefunction solution...
some context Problem 3: Use simple kinetic theory of gases discussed in section 1.3.2 as well...
some context
Problem 3: Use simple kinetic theory of gases discussed in section 1.3.2 as well as Fourer's law of condustion to prove: 2 R373 D11 = 3113/202pm Dal We were unable to transcribe this imageof a nes. the xed the led negligible The following assumptions about the structure of the cases are made in order to investigate the statistical rules of the random motion of the molecules: The size of the gas molecules is negligible compared with the distance...
1. The energy levels of a quantum harmonic oscillator are given by E Planck constant, w is the frequency of oscillation and n-0,1,2, Determine the following: (a) Show that the one-particle partition function is given by 211-exp-Bhu) oan 1 (1 Hint you will need to use the following formula for a geometric progression: (b) Show that the internal energy is given by (c) Show that the Helmoltz free energy is given by 1 In(1 exp Bha) (d) Show that the...
question no 4.22, statistical physics by Reif Volume 5
4.92 Mean energy of a harmonic oscillator A harmonic oscillator has a mass and spring constant which are such that its classical angular frequency of oscllation is equal to w. In a quantum- mechanical description, such an oscillator is characterized by a set of discrete states having energies En given by The quantum number n which labels these states can here assume all the integral values A particular instance of a...
Quantum, 1D harmonic oscillator. Please answer in full.
Thanks.
Q3. The energy levels of the 1D harmonic oscillator are given by: En = (n +2)ha, n=0. 1, 2, 3, The CO molecule has a (reduced) mass of mco = 1.139 × 10-26 kg. Assuming a force constant of kco 1860 N/m, what is: a) The angular frequency, w, of the ground state CO bond vibration? b) The energy separation between the ground and first excited vibrational states? 7 marks] The...
1. An ideal (frictionless) simple harmonic oscillator is set into motion by releasing it from rest at X +0.750 m. The oscillator is set into motion once again from x=+0.750 m, except the oscillator now experiences a retarding force that is linear with respect to velocity. As a result, the oscillator does not return to its original starting position, but instead reaches = +0.700 m after one period. a. During the first full oscillation of motion, determine the fraction of...
4. (a) The energy states of Landau levels are given by where wc is the cyclotron frequency Using this and the 2D density of states given by where m is the carrier effective mass, deduce the degeneracy of a Landau Level Sketch these Landau levels on a graph of number n(E) verses energy (E), and indicate the position of the Fermi Energy for a filling factor of 8 4 (b) Sketch the band diagram for a heterojunction between p-type AlGaAs...
(30) Given the equilibrium bond length of CO is 1.138, explore population fractions (Eq. 2) of the ground state and first 15 pure rotational excited states relative to the ground state (where {=0). Mathematica is recommended. Do this at 298 K and at 100 K. Comment on how the results differ compared to part a). 1) In the application of quantum mechanical and statistical mechanical principles to samples containing large numbers of species (e.g. macroscopic samples of molecules), there is...
can you explaination for thes questions how did we got these
right answers. Thankyou!
w many photons of light with frequency 5.50 x 1015 Hz are required to provide 1 kJ of energy? 3364 x 10-18 2. What is the wavelength of a bullet that is 0.450 g traveling at 2000. m/s? A) 2000 nm B) 2.74 x 1020 C) 4.56 x 10 D) 1.65x 10 E)3.84x 10 B) 2/94 x 10-24 m C) 7.36 x 104 m D) 7.36...
1 Particle in a Box with a Bump (based on B&J 4.11) Consider a particle of mass m in a 1-D double well with potential given by Vo, 05\x\<b V(x) = { 0, b<\x<c 100, [x]>c . We will study the lowest energy states, for which 0 <E<V, corresponding to tunnelling between the two wells. (a) Write down the time-independent Schödinger equation in the three regions -c<x<-b, –b< <b, and b< I< c. Write down the most general wavefunction solution...
some context
Problem 3: Use simple kinetic theory of gases discussed in section 1.3.2 as well as Fourer's law of condustion to prove: 2 R373 D11 = 3113/202pm Dal We were unable to transcribe this imageof a nes. the xed the led negligible The following assumptions about the structure of the cases are made in order to investigate the statistical rules of the random motion of the molecules: The size of the gas molecules is negligible compared with the distance...
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