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2. Prove Find the value of the normalization constant A for the wave function y Axe 2. Prove Find the value of the normalization constant A for the wave function y Axe
3- A one-dimensional harmonic oscillator wave function is ψ(x) = Axe-bx2 a) Find the total energy E b) Find the constant b c) Find the normalization constant A. d) Find the expectation value of x, e) Find the uncertainty in x, Ох. f) Find the expectation value of p g) Find the uncertainty in p, Op For the Hamiltonian matrix shown below:
3- A one-dimensional harmonic oscillator wave function is ψ(x) = Axe-bx2 a) Find the total energy E b)...
A particle is described by the wave function where A0. Find the normalization constant A.
A particle is described by the wave function where A0. Find the normalization constant A.
A. Normalize the wave function Ψ=Ae^(-ax^2) where A is the normalization constant and a is an integer. A= ? B. What is the expected value of the momentum? <p> = ?
lsa(1) lsB(1) 1Isa(2) 1sja 7. Consider this two-electron wave function: ψ-C Write the expression for ψ that comes from expanding the determinant. Find the normalization constant, C. The 1s orbitals are orthonormal, and so are the spin orbitals. a) b) Using your answer from (a), show that the wave function factors into a spin part and a spatial part. Hint: It may help to rewrite each spin orbit so its spatial and spin factors are clearer. For instance, rewrite Isa...
consider a particle with the wave function v(x)=N[sin(x)+sin(6x)] and the boundary condiitons 0<x<pi. Find the value of normalization constant
A linear combination of 2 wave functions for the same system is
also valid wave function .find the normalization constant B for the
combination
of wave functions for n=1 and n=2 of a particle in a box L
wide.
V = B(sinc/L + Sin2/L)
Find the normalization constant c and the marginal pdf's for the following joint pdf fxy(x, y) = ce-*e-y for 0 Sysx < 0
Problem 1. Wave function An electron is described by a wave function: for x < 0 *(z) = { ce Ce-s/1(1 – e-3/4) for x > 0 : where I is a constant length, and C is the normalization constant. 1. Find C. 2. Where an electron is most likely to be found; that is, for what value of x is the prob: bility for finding electron largest? 3. What is the average coordinate 7 of the electron? 4. What...
Consider a particle confined to one dimension and positive with the wave function Nxear, x20 x<0 0 where N is a real normalization constant and α is a real positive constant with units of (length)-1. For the following, express your answers in terms of α: a) Find the normalization constant N. What are the units of your result and do they make sense? b) What is the most probable location to find the particle, or more precisely, at what z...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...