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The wave function of the particle lies in which region?
a) x > 0
b) x < 0
c) 0 < X < L
d) x > L
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- A particle moving in one dimension has the wave function Y(x,t) = Aeli(ax-bt)] %3D where a and b are constants. What is the potential field V(x) in which the particle is moving?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 XQUESTION 3 Consider a wavefunction defined by: xL The product of the normalisation constant A and ,7, is equal to: а. 30 b. 15 V12 С. 24
- n=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 0QUESTION 6 Consider a 1-dimensional particle-in-a-box system. How long is the box in radians if the wave function is Y =sin(8x) ? 4 4л none are correct T/2 O O OGiven a Gaussian wave function: Y(x) = e-mwx?/h %D Where a is a positive constant 1) Find the normalization (if the wave function is not normalized) 2) Determine the mean value of the position x of the particle : i 3) Determine the mean value of x? : x2 4) Determine the value of Ax = V(x2) – (x)² -2. Find the best bound on Egs for the one-dimensional harmonic oscillator using the trial wave function of the form A (x): x2 + b2 Where A is determined by normalization and b is an adjustable parameterGiven a Gaussian wave function: Y(x) = (1/a)-1/4e-ax²/2 Where a is a positive constant 1) Find the normalization (if the wave function is not normalized) 2) Determine the mean value of the position x of the particle : x 3) Determine the mean value of x? : x? 4) Determine the value of Ax = /(x²) – (x)²A particle is described by the following function: A for 1The wavefunction of a particle in a box is represented by: O a. b. C. d. 2 nx -√√() sin a y(x) = 2 ηπ -√(1) sin a a y(x) = 2 -A = sin a a y(x): X a 2 w=√( =) y(x) = sin a a1-D Harmonic Oscillator Given the ff: Potential Energy: V(x) = //kx² Ground State Wave Function: 0(x) = Ce-a² What is the value of C?2. A three-state system has energy eigenfunctions $1(x), Þ2(x) and $3(x) with corresponding energy eigenvalues -ħw, 0, ħw respectively. The system is in the initial state of wavefunction p(x, 0) = c1 $1(x) + c2$2(x) + 2c2¢2(x) where w, C1, C2 are positive real constants. If the expectation value of the Hamiltonian in this state is equal to -0.64hw a. Obtain c1 and c2 b. Write the normalized wavefunction (x, t) c. Determine the uncertainty in energy AE in the state of wavefunction (x, t) d. What is the probability of measuring the energy ħw at time t?SEE MORE QUESTIONSRecommended textbooks for youPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
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