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- 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 conditionProblem 1. A free particle has the initial wave function (x, 0) = Ae-a.x² where A and a are constants (a is real and positive). (a) Normalize (.r. 0). (b) Find (x,1). (c) Find |(x, t) ².0.|A particle is confined in a potential V(x)= -2x². A. The particle is at the second excited ground state. Please write down the wave function. (normalized) B. What the energy of the state. C. Write down the probability function.
- If the particle described by the wavefunction 2a /ae x>0 is trapped in a y(x) = x<0 box of dimension: [on=2 35 L FIGURE 1.0 1. FIGURE 1.0 shows a particle of mass m moves in x-axis with the following potential: V(x) = { 0, for 0Physics Department PHYS4101 (Quantum Mechanics) Assignment 2 (Fall 2020) Name & ID#. A three-dimensional harmonic oscillator of mass m has the potential energy 1 1 1 V(x.y.2) = ; mw*x² +mwży² +=mw;z? where w1 = 2w a. Write its general eigenvalues and eigenfunctions b. Determine the eigenvalues and their degeneracies up to the 4th excited state c. The oscillator is initially equally likely found in the ground, first and second excited states and is also equally likely found among the states of the degenerate levels. Calculate the expectation values of the product xyz at time tProblem 1. Using the WKB approximation, calculate the energy eigenvalues En of a quantum- mechanical particle with mass m and potential energy V (x) = V₁ (x/x)*, where V > 0, Express En as a function of n; determine the dimensionless numeric coefficient that emerges in this expression.Y (X) = B exp (-^ ]x| + iwx) Q3: Consider a system has the wavefunction v(x)-8 exp(-e+Aex where 2 and w are real constants a) Determine the normalization constant B b) Determine the expectation value of X and XSuppose Fuzzy, a quantum-mechanical duck, lives in a world in which h = 2 J s. Fuzzy has a mass of 1.90 kg and is initially known to be within a pond 1.00 m wide. (a) What is the minimum uncertainty in the duck's speed? m/s (b) Assuming this uncertainty in speed to prevail for 4.90 s, determine the uncertainty in Fuzzy's position after this time. mGiven: For sake of simplicity, let us consider a particle with mass, m, in one dimension trapped in an infinite square well potential. The bottom of the potential well has zero potential energy, and the particle is known to be confined between 00 A physical system is described by a two-dimensional vector space with Hamiltonian operator Ĥ given by Ĥ = (_) where a is a constant. At time t = 0, the system is prepared in state (t = 0)) = -i2.5 0 determine the expectation value (Ŝ) at time t = πħ/(4x). O a. 2.17 O b. -2.50 O c. -1.25 O d. 2.50 O e. 5.00 0 (¹). For operator $ = (2 i2.5I The a wave function for a system is (x, t) = x e-(x+iat) , find the energy and the potential for the system.SEE MORE QUESTIONSRecommended textbooks for youCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University PressPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio…PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSONCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University PressPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio…PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON