(a) Find ψ(x, t) and P(En) at t > 0 for a particle in a one-dimensional...
(a) Find ψ(x, t) and P(En) at t > 0 for a particle in a one-dimensional infinite potential well with walls at x = 0 and x = a, for the following initial state.
ii. ψ(x, 0) = A(exp(iπ(x − a)/a) − 1)
(b) If measurement of E at 5s, finds that E = 4π^2 h(bar)^ 2 /(2ma^2 ), what is ψ(x, t) at t > 5s for the initial state?
Homework Answers
Add Answer to:
(a) Find ψ(x, t) and P(En) at t > 0 for a particle in a
one-dimensional...
At time t = 0, a mass-m particle in a one-dimensional potential well is in a...
At time t = 0, a mass-m particle in a one-dimensional potential well is in a state given by the normalised wave function (x, 0) =3/2eAl2| | -ao x << 0, realU>0. Find the potential energy V = the energy eigenvalue E. Fix zero energy according to the convention V(x) » 0 for ao. Is there a delta function singularity at x0? V (x) for which this is an energy eigenstate and determine [6]
At time t = 0, a...
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0,...
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0, otherwise where a and A are positive real numbers. The particle is in a zero (or constant) potential environment since it is a free particle a) Determine A from normalization. b) Determine φ(p) = Φ(p,0), the time-zero momentum representation of the particle state. What is Φ(p,t)? Sketch φ(p). Locate the global maximum and the zeros of φ(p). Give the expression for the zeros (i.e.,...
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite...
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite square well -a < x < a is given by 2 sin2 V inside the well and zero outside. Find the probability that a measurement of energy yields the eigenvalue En. (Hint: use data on page 6.) [6] Useful Data and Formulas = 1.60 x 10-19 C Elementary charge e h/2T=1.05 x 10-34 Js Planck's constant 3.00 x 108 m s-1 Speed of light...
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the dou...
quantum mechanics
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the doubly degenerate eigenstates are: Ιψη, p (x,y))-2sinnLx sinpry for 0 < x, y < L elsewhere and their eigenenergies are: n + p, n, p where n, p-1,2, 3,.... Calculate the energy of the first excited state up to the first order in perturbation theory due to the addition of: 2 2
Consider a particle confined in two-dimensional box with infinite...
The one-dimensional wave function for a particle over all space... may be exp ressed as a) Apply the momentum and energy Operators to ψ ( ie, p Ψ & ΕΨ ) as to verify the following pshk and Es...
The one-dimensional wave function for a particle over all space... may be exp ressed as a) Apply the momentum and energy Operators to ψ ( ie, p Ψ & ΕΨ ) as to verify the following pshk and Eshω Schrodinger sequation...-Nay equation... Ew andthen wufythefollowing: b) Substitute w into 2m ax E-Pi 2m
The one-dimensional wave function for a particle over all space... may be exp ressed as a) Apply the momentum and energy Operators to ψ ( ie, p...
Questions 1 - 5 deal with a particle in a one-dimensional infinite square well of width...
Questions 1 - 5 deal with a particle in a one-dimensional infinite square well of width a where 0, 0 SX Sa V(x) = 100, Otherwise. The stationary states are Pn(x) = sin(**) with energies En = "forn = 1,2,3.. Question 1 (14 pts) Which of the following is correct? A. The Hilbert space for this system is one dimensional. B. The energy eigenstates of the system form a ID Hilbert space. C. Both A and B are correct. D....
Al hamonic poteantial with cigcnstat) definedb Consider a particle in a one-dimensional harmonic ...
al hamonic poteantial with cigcnstat) definedb Consider a particle in a one-dimensional harmonic potential with eigenstates |n〉 defined by A n)-E n . If the particle is initially in an equal superposition ofits groundstate and first excited state: |ψ(t-0 2. excited state: Ive-o)- )-11) (a) According to the time-dependent Schrodinger equation, what is the wavefunetion of the particle at a later time t (b) Find the expectation value of position as a function of time for the particle. Hint: use...
V(x) = ㆀ other iE t 72 T where En= Given the initial state 0 Ψ(x,...
V(x) = ㆀ other iE t 72 T where En= Given the initial state 0 Ψ(x, 0) =-sin 5 L Normalize to find A, find the (allowable) eigenvalues and their corresponding probability of obtaining therm Calculate the average energy and determine the probability of finding the system at time tin the state an
1l] A particle with mass m and energy E is inside a square tube with infinite potential barriers at x-o, x-a, y 0,...
1l] A particle with mass m and energy E is inside a square tube with infinite potential barriers at x-o, x-a, y 0, y a. The tube is infinitely long in the +z-direction. (a) Solve the Schroedinger equation to derive the allowed wave functions for this particle. Do not try to normalize the wave functions, but make sure they correspond to motion in +2-direction. (b) Determine the allowed energies for such a particle. (c) If we were to probe 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...
At time t = 0, a mass-m particle in a one-dimensional potential well is in a state given by the normalised wave function (x, 0) =3/2eAl2| | -ao x << 0, realU>0. Find the potential energy V = the energy eigenvalue E. Fix zero energy according to the convention V(x) » 0 for ao. Is there a delta function singularity at x0? V (x) for which this is an energy eigenstate and determine [6]
At time t = 0, a...
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite square well -a < x < a is given by 2 sin2 V inside the well and zero outside. Find the probability that a measurement of energy yields the eigenvalue En. (Hint: use data on page 6.) [6] Useful Data and Formulas = 1.60 x 10-19 C Elementary charge e h/2T=1.05 x 10-34 Js Planck's constant 3.00 x 108 m s-1 Speed of light...
quantum mechanics
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the doubly degenerate eigenstates are: Ιψη, p (x,y))-2sinnLx sinpry for 0 < x, y < L elsewhere and their eigenenergies are: n + p, n, p where n, p-1,2, 3,.... Calculate the energy of the first excited state up to the first order in perturbation theory due to the addition of: 2 2
Consider a particle confined in two-dimensional box with infinite...
The one-dimensional wave function for a particle over all space... may be exp ressed as a) Apply the momentum and energy Operators to ψ ( ie, p Ψ & ΕΨ ) as to verify the following pshk and Eshω Schrodinger sequation...-Nay equation... Ew andthen wufythefollowing: b) Substitute w into 2m ax E-Pi 2m
The one-dimensional wave function for a particle over all space... may be exp ressed as a) Apply the momentum and energy Operators to ψ ( ie, p...
Questions 1 - 5 deal with a particle in a one-dimensional infinite square well of width a where 0, 0 SX Sa V(x) = 100, Otherwise. The stationary states are Pn(x) = sin(**) with energies En = "forn = 1,2,3.. Question 1 (14 pts) Which of the following is correct? A. The Hilbert space for this system is one dimensional. B. The energy eigenstates of the system form a ID Hilbert space. C. Both A and B are correct. D....
al hamonic poteantial with cigcnstat) definedb Consider a particle in a one-dimensional harmonic potential with eigenstates |n〉 defined by A n)-E n . If the particle is initially in an equal superposition ofits groundstate and first excited state: |ψ(t-0 2. excited state: Ive-o)- )-11) (a) According to the time-dependent Schrodinger equation, what is the wavefunetion of the particle at a later time t (b) Find the expectation value of position as a function of time for the particle. Hint: use...
V(x) = ㆀ other iE t 72 T where En= Given the initial state 0 Ψ(x, 0) =-sin 5 L Normalize to find A, find the (allowable) eigenvalues and their corresponding probability of obtaining therm Calculate the average energy and determine the probability of finding the system at time tin the state an
1l] A particle with mass m and energy E is inside a square tube with infinite potential barriers at x-o, x-a, y 0, y a. The tube is infinitely long in the +z-direction. (a) Solve the Schroedinger equation to derive the allowed wave functions for this particle. Do not try to normalize the wave functions, but make sure they correspond to motion in +2-direction. (b) Determine the allowed energies for such a particle. (c) If we were to probe 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...
Most questions answered within 3 hours.
-
Description: Operating your business with a business mindset is
the key here. You can only wear...
asked 6 minutes ago -
Mooncents Coffee Shop has just opened, and on the first 6 days
of business, the number...
asked 7 minutes ago -
(a) Find ?z such that the proportion of observations that are
less than ?z in a...
asked 13 minutes ago -
Discuss the advantages and disadvantages of a gather society and
an agrarian society in regard to...
asked 36 minutes ago -
What is compliance and how it is related to information
security?
What are the differences between...
asked 35 minutes ago -
Indicate the
amino acid
sequence of the protein encoded by the following mRNA molecule.
Use the...
asked 41 minutes ago -
Weihong Corporation is about to emerge from a Chapter 11
reorganization. Assets of the emerging entity...
asked 40 minutes ago -
Give an example of a successful company in different parts of
the world that have used...
asked 42 minutes ago -
Implement a class CSVReader that reads a CSV file, and provide
methods:
int numbOfRows()
int numberOfFields(int...
asked 41 minutes ago -
Suppose that A and B are mutually exclusive and complementary
events, such that P(A)=0.7 and P(B)=0.3....
asked 1 hour ago -
What parallels can you draw from the African-American performers
Bill" Bojangles" Robinson, James Brown and Michael...
asked 59 minutes ago -
What cognitive disorder does the individual in Oliver
Sacks' book 'The Man Who Mistook His Wife...
asked 1 hour ago