3The eigenstates y y of a quantum system are associated, respectively, to the1' 2'eigenvalues ε1, 2, 3 of the observable E. The system is prepared in such a way that itsstate is described by the wavefunction:Ψ=1-2Assuming the w; are individually normalised, determine the normalisation factor N. Entera number into the empty box below.N=Calculate the probability of obtaining ε in a measurement of E. Enter a number, specifiedto two significant figures, in the box below.probability of obtaining &2 =

Answered: 3 The eigenstates y y of a quantum…

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter6: Quantum Mechanics In One Dimension

Section: Chapter Questions

Problem 29P

See similar textbooks

Similar questions

catum eigenvalues and eigen states look like? B) A particle of mass m is placed in 1-D harmonic oscillator potential. At t-0, its wave function is P(x,0). At t=27/ its wave function will be: 1) Y(x,0) 2) - (x,0) 3) - Y(x,0) 4) (27/0) Y(x,0).'
A particle in the ground state of the quantum harmonic oscillator has a wavefunction that can be written as found in image where a = mω/hbar , and where N, m and ω are all constants. For this particle: a) Find an expression for the normalization constant N, in terms of a. b) Derive an expression for the uncertainty in the momentum, ∆p. N.B. You may wish to refer to the Appendix when answering this question.
Suppose a harmonic oscillator is subject to a perturbation av = Ahw (&/#0)* . where ro = mw/h is the length scale of the problem. a) Use Rayleigh-Schrödinger perturbation theory to find the first and second order corrections to the energies of the n'th level. b) Discuss the applicability of the perturbative approach for states with large n,
6. A set of N classical oscillators in one dimension is given by the Hamil- tonian N Σ (2²m² ² + 1/ mw³²q² ) . i=1 H=Σ Using the formalism of the canonical ensemble in classical phase space, obtain expressions for the partition function, the energy per oscillator, the entropy per oscillator, and the specific heat. Compare with the results from the classical limit of the quantum oscillator. Calculate an expression for the quadratic deviation of the energy as a function of temperature.
11 Q Search | Start conversation Close D QM-assignment-3.pdf 1. An electron is moving freely inside a one-dimensional infinite potential well with walls at x = 0 and x = a. The size of the box is quadrupled suddenly. Consider that the particle is in nth quantum state initially before perturbation. Obtain an expression for the the probability of finding the particle in the mth state of the second well. Simplify the expression for the following cases: (i) m and n are odd integers (ii) m is even and n is odd (iii) m = n =1 (iv) n=1 and m=2
The potential energy Uis zero in the interval 0
A particle of mass m is contained in a one-dimensional infinite well extending from L to x=- 2 L The particle is in its ground state given by ø.(x)= /2/L cos(zx/L). X = - The walls of the box are moved suddenly to form a box extending from x = -L to x= L. what is the probability that the particle will be in the ground state after this sudden expansion?
A particle in a box is in the ground level. What is the probability of finding the particle in the right half of the box? (Refer to Fig. , but don’t evaluate an integral.) Is the answer the same if the particle is in an excited level? Explain.
Here are the properties of the GaAs quantum well in the figure. v0 = 100 ??? L = 200 Å ?∗ = 0.067 m* Find the energy values of the first three levels of this well. Corresponding wave functions Draw the graph. It is assumed that the effective mass m* given for the well is also valid for barriers. please. The material of the barrier is not important here. The important thing is the V0 potential.
a. Calculate the minimum uncertainty in the position of an electron in meters, if its velocity has been measured to within 2.34e-06 m/s. For the mass of an electron use 9.10938356 × 10-31 kg and for huse 1.0545718 x 10-34 Js. m b. 44 = 141² = ² represents a: O the pitchfork operator O probability density O numerov program O wave function c. The sum of all the little bits of probability over possible measurements that can be made (i.e. over all space): S4²4 = 1 is called: O the quantum condition O the normalization condition O the human condition O the eignen condition
the ground state wavefunction of a quantum mechanical simple harmonic oscillator of mass m and frequency, which is given by: Question mw where a = the potential is V(x) = mw²x² and N is given by: N =) 9 ax² ¡Ent Yo (x, t) = Ne ze By substituting into the time-dependent Schrödinger equation, prove that the ground state energy, Eo, is given by: Eo ħw 2
Consider an electron trapped in a 20 Å long box whose wavefunction is given by the following linear combination of the particle's n= 2 and n = 3 states: .= ((x,tvי 2nx sin V10 ´3x - sin 4 where E, a 2ma² a. Determine if this wavefunction is properly normalized. If not, determine an appropriate value for a normalization constant. b. Show that this is not an eigenfunction to the PitB problem. What are the possible results that could be returned when the energy is measured and what are the probabilities of measuring each of these results? c. Calculate Y(x,1) = ¥° (x,1)¥ (x.1) and sketch what this looks like for t=0, 3th 2xh ,and 1 (E,-E,) You will likely want 2(E,- E.) (E,-E.)' to use a graphing program such as Excel, Mathematica, or Matlab for this. What happens to the most likely position to find the particle as time progresses? Does it move? If so, with what frequency does it move? 2(E, – E,)'

SEE MORE QUESTIONS

Recommended textbooks for you

Modern Physics

Physics

ISBN:

9781111794378

Author:

Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:

Cengage Learning

University Physics Volume 3

Physics

ISBN:

9781938168185

Author:

William Moebs, Jeff Sanny

Publisher:

OpenStax

Physics for Scientists and Engineers with Modern …

Physics

ISBN:

9781337553292

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Modern Physics

Physics

ISBN:

9781111794378

Author:

Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:

Cengage Learning

University Physics Volume 3

Physics

ISBN:

9781938168185

Author:

William Moebs, Jeff Sanny

Publisher:

OpenStax

Physics for Scientists and Engineers with Modern …

Physics

ISBN:

9781337553292

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS