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II.6. The wave function of a particle in a 1D rigid box (infinite potential well) of...
For a one-dimensional particle in a box system of length L (infinite potential well) with 2/L sin (nnx)/L where n= 1,2,...
For a one-dimensional particle in a box system of length L (infinite potential well) with 2/L sin (nnx)/L where n= 1,2,3.. b(x) at which n value(s) the probability of finding the particle is the highest at L/2? a(x) 3(x) 2(x) (x) L
The measured ionization energy of the 2s1 electron of Lithium is 5.39eV, what is the effective...
The measured ionization energy of the 2s1 electron of Lithium is 5.39eV, what is the effective charge Zeff of the Lithium nucleus for this electron? II.2. How fast must an object move before its length appears to be contracted to one-half its proper length? II.3. A distant galaxy is moving away from the Earth at such high speed that a spectrum line at a wavelength of 300nm is recorded at 600nm. What is the speed of the galaxy relative to...
1. A particle, initially (t -> 0) in the ground state of an infinite, 1D potential...
1. A particle, initially (t -> 0) in the ground state of an infinite, 1D potential box with walls at r 0 and = a, is subjected at time t = 0 to a time-dependent perturbation V (r, t) et/7, with eo a small real number a) Calculate to first order the probability of finding the particle in an excited state for t 0. Consider all final states. Are all possible transitions allowed? b) Examine the time dependence of the...
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically ab...
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically about the origin of the x-axis. A measurement of energy is made and the particle is found to have the ground state energy: 2ma The walls of the box are expanded instantaneously, doubling the well width symmetrically about the origin, leaving the particle in the same state. a) Sketch the initial potential well making it symmetric about x - 0 (note this is different...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a)...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
Exercise 10.14 A particle is initially in its ground state in an infinite one-dimensional potential box...
Exercise 10.14 A particle is initially in its ground state in an infinite one-dimensional potential box with sides at x = 0 and x a. If the wall of the box at x-a is suddenly moved to x = 10a, calculate the probability of finding the particle in (a) the fourth excited (n = 5) state of the new box and (b) the ninth (n 10) excited state of the new box.
Particle with a speed bump Consider our old friend the 1D particle in the box, except...
Particle with a speed bump Consider our old friend the 1D particle in the box, except now with a speed bump in the box so the potential now is given by L and L < x < L 0, Vo 0 x V (x) otherwise (a) Calculate the first order correction to the ground state (n = 1) and first excited state (n = 2) energies (b) Calculate the first order correction to the ground state wave function in terms...
DApdr Q2. An electron is trapped in an one dimensional infinite potential well of length L...
DApdr Q2. An electron is trapped in an one dimensional infinite potential well of length L Calculate the Probability of finding the electron somewhere in the region 0 <xLI4. The ground state wave function of the electron is given as ㄫㄨ (r)sin (5 Marks) O lype hene to search
A particle is confined to a one-dimensional box (an infinite well) on the x-axis between x...
A particle is confined to a one-dimensional box (an infinite well) on the x-axis between x = 0 and x L. The normalized wave function of the particle when in the ground state, is given by A. What is the probability of finding the particle between x Eo, andx,? A. 0.20 B. 0.26 C. 0.28 D. 0.22 E. 0.24
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x)...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...
For a one-dimensional particle in a box system of length L (infinite potential well) with 2/L sin (nnx)/L where n= 1,2,3.. b(x) at which n value(s) the probability of finding the particle is the highest at L/2? a(x) 3(x) 2(x) (x) L
1. A particle, initially (t -> 0) in the ground state of an infinite, 1D potential box with walls at r 0 and = a, is subjected at time t = 0 to a time-dependent perturbation V (r, t) et/7, with eo a small real number a) Calculate to first order the probability of finding the particle in an excited state for t 0. Consider all final states. Are all possible transitions allowed? b) Examine the time dependence of the...
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically about the origin of the x-axis. A measurement of energy is made and the particle is found to have the ground state energy: 2ma The walls of the box are expanded instantaneously, doubling the well width symmetrically about the origin, leaving the particle in the same state. a) Sketch the initial potential well making it symmetric about x - 0 (note this is different...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
Exercise 10.14 A particle is initially in its ground state in an infinite one-dimensional potential box with sides at x = 0 and x a. If the wall of the box at x-a is suddenly moved to x = 10a, calculate the probability of finding the particle in (a) the fourth excited (n = 5) state of the new box and (b) the ninth (n 10) excited state of the new box.
Particle with a speed bump Consider our old friend the 1D particle in the box, except now with a speed bump in the box so the potential now is given by L and L < x < L 0, Vo 0 x V (x) otherwise (a) Calculate the first order correction to the ground state (n = 1) and first excited state (n = 2) energies (b) Calculate the first order correction to the ground state wave function in terms...
DApdr Q2. An electron is trapped in an one dimensional infinite potential well of length L Calculate the Probability of finding the electron somewhere in the region 0 <xLI4. The ground state wave function of the electron is given as ㄫㄨ (r)sin (5 Marks) O lype hene to search
A particle is confined to a one-dimensional box (an infinite well) on the x-axis between x = 0 and x L. The normalized wave function of the particle when in the ground state, is given by A. What is the probability of finding the particle between x Eo, andx,? A. 0.20 B. 0.26 C. 0.28 D. 0.22 E. 0.24
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...
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