suppose a particle in a bow of length L in its ground state and is a...
suppose a particle in a bow of length L in its ground state and is a normalized wave function, what is the average value of the hamiltonian squared?
Homework Answers
Average value of hamiltonian
square means its expectation value . And for particle in box
wavefunction is normalised and you need to worry about its
conjugate becoz in conjugate is same . And caculations are
simple...
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suppose a particle in a bow of length L in its ground state and
is a...
A particle is in the ground state of a box of length L (from -L/2 to...
A particle is in the ground state of a box of length L (from -L/2 to L/2). Suddenly the box expands symmetrically to twice its size (from -L to L), leaving the wave function undisturbed. Show that the probability of finding the particle in the ground state of the new box is (8/3pi)^2.
2. Now consider a particle in the ground state of the harmonic oscillator. ok gives the...
2. Now consider a particle in the ground state of the harmonic oscillator. ok gives the wave function for the ground state, but not the value of the constant A. Determine what it has to be if the ground state is normalized. (b) Suppose a classical particle has an energy equal to the ground state energy E. This particle will, of course, oscillate back and forth as though it were attached to a spring. What would its turning points be?...
64 Consider a particle in a one-dimensional box in the ground state v, and the first...
64 Consider a particle in a one-dimensional box in the ground state v, and the first excited state , described by the wave functions listed below. For each wave function, calculate the expec- tation value of the position (x), the expectation value of the position squared (), the expecta- tion value of the momentum (p), and the expectation value of the momentum squared (p2). 2 . 2x Ossa 0sxSa (b) Y2(x) = Vasin-
A particle in an infinite well of width L is in its ground state. a) If...
A particle in an infinite well of width L is in its ground state. a) If L is 30 cm, what is the ground state energy? (3 marks) Where is the particle most likely to be found? Use sketching to further explain. (4 marks)
Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is...
Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by Knowing that the ground state of the particle at a certain instant is described by the wave function mw 1/4 _mw2 Th / calculate (for the ground state): a) The mean value of the position <x> (2 marks) b) The mean value of the position squared < x2 > (2 marks) c) the mean value of the momentum <p> (2...
8. Consider one electron in a 1D box of side L. Its wavefunction is given by...
8. Consider one electron in a 1D box of side L. Its wavefunction is given by из where ф1(x), фг(x), and фз(x) are the first 3 eigenfunctions of the Hamiltonian, H, of a particle in a 1D box, 2m dx2 a) Is Ψ(x) normalized? If it is not normalized it, normalize it! b) Is Ψ(x) an eigenfunction of A? If it is an eigenfunction, what is the 9. A linear polyene contains 8 -electrons, and absorbs light with412 nm. b)...
A particle moves in 5 dimensional space (x, y, z, u, v). Its Hamiltonian is given...
A particle moves in 5 dimensional space (x, y, z, u, v). Its
Hamiltonian is given by
where the space is infinite in all directions except v which is
confined between v = 0 and v = a. Assume that the wave function
vanishes at v = 0 and v = a. Further,
= |E| 1 /~ 2 , where |E1| is the absolute value of the Hydrogen
ground state energy.
(d) What are the eigenstates of this Hamiltonian in...
a. A particle of mass m moves freely on a line of length a il In...
a. A particle of mass m moves freely on a line of length a il In the same diagram, draw the wave function and the squared wave function for the 2nd excited state of the particle. (4 marks) ii. What is the difference between classical and quantum mechanical behavior of the particle in such a box? (3 marks) Hi. Write the expression for the energy of the particle moving freely in a box of sides a, b and c. (2...
1. Suppose we didn't actually know the wave functions for a particle in a box. Reasonable...
1. Suppose we didn't actually know the wave functions for a particle in a box. Reasonable guesses for the ground- and first-excited-state wave functions might be functions of the form 1 = a y (1 - y) 02 = by (y-c)(y-1), where y = (x/L), L is the length of the box, and a, b, and care constants. (a) These functions have quite a number of features that make them sensible guesses. Sketch both functions and list these special features....
The answer is attached for reference HW15.3 A particle in a box of length L is...
The answer is attached for
reference
HW15.3 A particle in a box of length L is in its ground state (n 1). The wall of the box is suddenly moved outward to x-2L. Calculate the probability that the particle will be found in the ground state of the expanded box. Determine the state of the expanded box most likely to be occupied by the particle.
A particle is in the ground state of a box of length L (from -L/2 to L/2). Suddenly the box expands symmetrically to twice its size (from -L to L), leaving the wave function undisturbed. Show that the probability of finding the particle in the ground state of the new box is (8/3pi)^2.
2. Now consider a particle in the ground state of the harmonic oscillator. ok gives the wave function for the ground state, but not the value of the constant A. Determine what it has to be if the ground state is normalized. (b) Suppose a classical particle has an energy equal to the ground state energy E. This particle will, of course, oscillate back and forth as though it were attached to a spring. What would its turning points be?...
64 Consider a particle in a one-dimensional box in the ground state v, and the first excited state , described by the wave functions listed below. For each wave function, calculate the expec- tation value of the position (x), the expectation value of the position squared (), the expecta- tion value of the momentum (p), and the expectation value of the momentum squared (p2). 2 . 2x Ossa 0sxSa (b) Y2(x) = Vasin-
A particle in an infinite well of width L is in its ground state. a) If L is 30 cm, what is the ground state energy? (3 marks) Where is the particle most likely to be found? Use sketching to further explain. (4 marks)
Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by Knowing that the ground state of the particle at a certain instant is described by the wave function mw 1/4 _mw2 Th / calculate (for the ground state): a) The mean value of the position <x> (2 marks) b) The mean value of the position squared < x2 > (2 marks) c) the mean value of the momentum <p> (2...
8. Consider one electron in a 1D box of side L. Its wavefunction is given by из where ф1(x), фг(x), and фз(x) are the first 3 eigenfunctions of the Hamiltonian, H, of a particle in a 1D box, 2m dx2 a) Is Ψ(x) normalized? If it is not normalized it, normalize it! b) Is Ψ(x) an eigenfunction of A? If it is an eigenfunction, what is the 9. A linear polyene contains 8 -electrons, and absorbs light with412 nm. b)...
A particle moves in 5 dimensional space (x, y, z, u, v). Its
Hamiltonian is given by
where the space is infinite in all directions except v which is
confined between v = 0 and v = a. Assume that the wave function
vanishes at v = 0 and v = a. Further,
= |E| 1 /~ 2 , where |E1| is the absolute value of the Hydrogen
ground state energy.
(d) What are the eigenstates of this Hamiltonian in...
a. A particle of mass m moves freely on a line of length a il In the same diagram, draw the wave function and the squared wave function for the 2nd excited state of the particle. (4 marks) ii. What is the difference between classical and quantum mechanical behavior of the particle in such a box? (3 marks) Hi. Write the expression for the energy of the particle moving freely in a box of sides a, b and c. (2...
1. Suppose we didn't actually know the wave functions for a particle in a box. Reasonable guesses for the ground- and first-excited-state wave functions might be functions of the form 1 = a y (1 - y) 02 = by (y-c)(y-1), where y = (x/L), L is the length of the box, and a, b, and care constants. (a) These functions have quite a number of features that make them sensible guesses. Sketch both functions and list these special features....
The answer is attached for
reference
HW15.3 A particle in a box of length L is in its ground state (n 1). The wall of the box is suddenly moved outward to x-2L. Calculate the probability that the particle will be found in the ground state of the expanded box. Determine the state of the expanded box most likely to be occupied by the particle.
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