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Recall that for the Harmonic oscillator: vmk h Where k 2/2 is the wavenumber and m is the particle mass. =n2R-2k (n-2k...
1. Anharmonic oscillator. Hydrogen bromide, 'HiBr, vibrates approximately according to a Morse potential VM(r) = Dell-e-w2De)1/2 (r-rej2 with De= 4.8 10 eV, re= 1.4 1 44Ă, and k= 408.4 N m-1. Wit...
1. Anharmonic oscillator. Hydrogen bromide, 'HiBr, vibrates approximately according to a Morse potential VM(r) = Dell-e-w2De)1/2 (r-rej2 with De= 4.8 10 eV, re= 1.4 1 44Ă, and k= 408.4 N m-1. With ω,-VRA, the energies of the stationary states in a Morse potential are En (hwo) 4D ho(n+ 1/2)- (n + 1/2)2. (A) On the same graph, plot the Morse potential and the harmonic potential as a function of bond length (from 0.7 Te to 2 re).(B) Describe the differences....
Anharmonic oscillator. Hydrogen bromide, H8Br, vibrates approximately according to a Morse potential VM(r) = Dell-e-ck/2De)i/2(r-re) , with De= 4.810 eV, = 1.4144 A, and k= 408.4 N m-1. With a0-Vk/a,...
Anharmonic oscillator. Hydrogen bromide, H8Br, vibrates approximately according to a Morse potential VM(r) = Dell-e-ck/2De)i/2(r-re) , with De= 4.810 eV, = 1.4144 A, and k= 408.4 N m-1. With a0-Vk/a, the energies of the stationary states in a Morse potential are En (n + 1/2)2. (A) On the same graph, plot the Morse potential and the harmonic potential as a function of bond length (from 0.7 to 2 %). Use the software of your choice to generate this plot. (B)...
One can assume a quantum mechanical harmonic oscillator model for the N-H stretching vibrations of the...
One can assume a quantum mechanical harmonic oscillator model for the N-H stretching vibrations of the peptide bonds. For the harmonic oscillator the energy levels are given by: E, = (V+})ħw where: W= /k/ u In the above express k is the force constant and u is the reduced mass. (a) Write the Schrödinger equation in terms of the reduced mass u, being sure to define all symbols. (b) Calculate the frequency of the infrared radiation absorbed by the N-H...
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of th...
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of the harmonic oscillator potential corresponding to energies Eo, E1 and E2 (a) Show that the wavefunction is normalised (b) If an observation of energy is made, what is the most likely value of energy and with what probability would it be obtained? (c) If the experiment is...
Consider a particle with mass m described by the Hamilton operator for a one-dimensional harmonic oscillator...
Consider a particle with mass m described by the Hamilton operator for a one-dimensional harmonic oscillator 2 Zm 2 The normalized eigenfunctions for Hare φη (x) with energies E,,-(n + 2) ha. At time t-0 the wavefunction of the particle is given by у(x,0)- (V3іфі (x) + ф3(x)). Now let H' be an operator given by where k is a positive constant. 1) Show that H' is Hermitian. 2) Express H' by the step-operators a+ and a 3) Calculate the...
Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness...
Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness coefficient of the oscillator and m is mass. Recall that the oscillation frequency iso,s:,k, / m In class we showed that Ψ0(x) Is an eigenfunction of the Hamiltonian, with an eigenvalue Eo (1/2)ha a) Normalize the wave function in Eq.(1) b) Graph the probability density. Note that a has units of length and measures the "width" of the wave function. It's easier to use...
A harmonic oscillator consists of a block attached to a spring (k = 400 N/m). The...
A harmonic oscillator consists of a block attached to a spring (k = 400 N/m). The mass is initially displaced to x_max = 0.128 m. At some later time, t, the block has the following kinematic variables: x = 0.100 m, v = -13.6 m/s, a = -123 m/s^2 a) find the frequency of oscillation b) the mass of the block c) the amplitude of the motion. d) and the total mechanical energy of the system.
tthe-independent Help: The operator expression dimensions is given by H 2m r ar2 [2] A particle of mass m is in a three-dimensional, spherically symmetric harmonic oscillator potential given by V...
tthe-independent Help: The operator expression dimensions is given by H 2m r ar2 [2] A particle of mass m is in a three-dimensional, spherically symmetric harmonic oscillator potential given by V(r)2r2. The particle is in the I-0 state. Noting that all eigenfunetions must be finite everywhere, find the ground-state radial wave-function R() and the ground-state energy. You do not have to nor oscillator is g (x) = C x exp(-8x2), where C and B are constants) harmonic malize the solution....
Select the correct PROLOG definition of powerof2/2, where powerof2(K,N) checks whether N is equal to 2K...
Select the correct PROLOG definition of powerof2/2, where powerof2(K,N) checks whether N is equal to 2K (A) powerof2(0,1);- !. powerof2(K,P):- K1 is K-1, powerof2(K1,P1), P is P1*K. (B) (C) powerof2(0,1);- !. powerof2(K,P);- powerof2(K1,P1), K1 is K-1, P is P1*2. powerof2(0,1):- !. powerof2(K,P):- powerof2(K,P), P is P1*2. powerof2(0,1);- !. powerof2(K,P):- K1 is K-1, powerof2(K1,P1), P is P1*2. (D) CA (B) (C) D
2. A damped harmonic oscillator with m 1.00 kg, k 2500 N/m, and b 42.4 kg/s...
2. A damped harmonic oscillator with m 1.00 kg, k 2500 N/m, and b 42.4 kg/s is subject to a driving force given by Fo cos wt. (a) what value of ω results in the maximum stead-state amplitude (ie, resonance)? (b) What is the quality factor Q of this oscillator?
1. Anharmonic oscillator. Hydrogen bromide, 'HiBr, vibrates approximately according to a Morse potential VM(r) = Dell-e-w2De)1/2 (r-rej2 with De= 4.8 10 eV, re= 1.4 1 44Ă, and k= 408.4 N m-1. With ω,-VRA, the energies of the stationary states in a Morse potential are En (hwo) 4D ho(n+ 1/2)- (n + 1/2)2. (A) On the same graph, plot the Morse potential and the harmonic potential as a function of bond length (from 0.7 Te to 2 re).(B) Describe the differences....
Anharmonic oscillator. Hydrogen bromide, H8Br, vibrates approximately according to a Morse potential VM(r) = Dell-e-ck/2De)i/2(r-re) , with De= 4.810 eV, = 1.4144 A, and k= 408.4 N m-1. With a0-Vk/a, the energies of the stationary states in a Morse potential are En (n + 1/2)2. (A) On the same graph, plot the Morse potential and the harmonic potential as a function of bond length (from 0.7 to 2 %). Use the software of your choice to generate this plot. (B)...
One can assume a quantum mechanical harmonic oscillator model for the N-H stretching vibrations of the peptide bonds. For the harmonic oscillator the energy levels are given by: E, = (V+})ħw where: W= /k/ u In the above express k is the force constant and u is the reduced mass. (a) Write the Schrödinger equation in terms of the reduced mass u, being sure to define all symbols. (b) Calculate the frequency of the infrared radiation absorbed by the N-H...
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of the harmonic oscillator potential corresponding to energies Eo, E1 and E2 (a) Show that the wavefunction is normalised (b) If an observation of energy is made, what is the most likely value of energy and with what probability would it be obtained? (c) If the experiment is...
Consider a particle with mass m described by the Hamilton operator for a one-dimensional harmonic oscillator 2 Zm 2 The normalized eigenfunctions for Hare φη (x) with energies E,,-(n + 2) ha. At time t-0 the wavefunction of the particle is given by у(x,0)- (V3іфі (x) + ф3(x)). Now let H' be an operator given by where k is a positive constant. 1) Show that H' is Hermitian. 2) Express H' by the step-operators a+ and a 3) Calculate the...
Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness coefficient of the oscillator and m is mass. Recall that the oscillation frequency iso,s:,k, / m In class we showed that Ψ0(x) Is an eigenfunction of the Hamiltonian, with an eigenvalue Eo (1/2)ha a) Normalize the wave function in Eq.(1) b) Graph the probability density. Note that a has units of length and measures the "width" of the wave function. It's easier to use...
A harmonic oscillator consists of a block attached to a spring (k = 400 N/m). The mass is initially displaced to x_max = 0.128 m. At some later time, t, the block has the following kinematic variables: x = 0.100 m, v = -13.6 m/s, a = -123 m/s^2 a) find the frequency of oscillation b) the mass of the block c) the amplitude of the motion. d) and the total mechanical energy of the system.
tthe-independent Help: The operator expression dimensions is given by H 2m r ar2 [2] A particle of mass m is in a three-dimensional, spherically symmetric harmonic oscillator potential given by V(r)2r2. The particle is in the I-0 state. Noting that all eigenfunetions must be finite everywhere, find the ground-state radial wave-function R() and the ground-state energy. You do not have to nor oscillator is g (x) = C x exp(-8x2), where C and B are constants) harmonic malize the solution....
Select the correct PROLOG definition of powerof2/2, where powerof2(K,N) checks whether N is equal to 2K (A) powerof2(0,1);- !. powerof2(K,P):- K1 is K-1, powerof2(K1,P1), P is P1*K. (B) (C) powerof2(0,1);- !. powerof2(K,P);- powerof2(K1,P1), K1 is K-1, P is P1*2. powerof2(0,1):- !. powerof2(K,P):- powerof2(K,P), P is P1*2. powerof2(0,1);- !. powerof2(K,P):- K1 is K-1, powerof2(K1,P1), P is P1*2. (D) CA (B) (C) D
2. A damped harmonic oscillator with m 1.00 kg, k 2500 N/m, and b 42.4 kg/s is subject to a driving force given by Fo cos wt. (a) what value of ω results in the maximum stead-state amplitude (ie, resonance)? (b) What is the quality factor Q of this oscillator?
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