b. Where is the particle most likely to be found? Explain why. Answer: x = 0...
4) A particle in an infinite square well 0 for 0
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...
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscillator, respectively. (a) Normalize (r, 0). (b) Find the wavefunction (r, t) at a later time t and hence evaluate (x, t) 2. Leave your answers involving expressions in to and ₁. c) sing the following normalized expression of...
help on all a), b), and c) please!! 1. A particle in an infinite square well has an initial wave function Alsin sin 4 0 < x < L otherwise s(x, t = 0) 0 (a) Find A so that the wavefunction is normalized. (b) Find '(z,t). (c) Find the expectation value(E) of the energy of ψ(x,t = 0). You may use the result mx n 2 0 1. A particle in an infinite square well has an initial wave...
A particle in an infinite square well has the initial wave function: (x,0)- A sin(x/a) (0 S a (a) (b) Determine A Find$(z,t) (Hint: You will need to break up this wavefunction into a superposition of pure states. Use orthogonality to find the coefficients.) (c) Calculate (x). Is it a function of time? (d) Calculate (H).
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
need help with this problem. please explain, thank you. 8. Consider a particle encountering a barrier with potential U = U, >0 between x = -a and x = a with incoming energy E > U. a) Write the symbolic wave functions before and after passing through the barrier (i.e., for xs-a and x>a; regions I and III). UN b) Write down the Schrodinger equation for the wave function in the middle (region II) where the potential is non-zero i.e.,...
You are given the following multivariate PDF (z, y, z) ES else fxx,z(x, y, z) = ) 0 where S-((x, y, z) | x2 + y2 + z2-1) (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of s....
Q 1: For particle in a box problem, answer the following questions, a) Why n=0 is not an allowed quantum number? b) En = 0 is not allowed for particle in a box, why? c) Ground state wavefunction is orthogonal to the first excited state wavefunction, what does it mean? Q 2: An electronic system that is treated as particle in 3-D box with dimensions of 3Å x 3Å x 4Å. Calculate the wavelength corresponding to the lowest energy transition...
(a) Sketch the region in the (x,y) plane where ??,?(?, ?) ≠ 0. (b) Find the marginal probability density functions ??(?) and ??(?) of ? and ? respectively. (c) Are X and Y independent? (d) Find P(Y>X). (e) Let y be some real number in the range 0 ≤ y ≤ 1. Find the conditional probability density function ??|?(?|?). (f) Find ?[?|? = ?] (where ? is some real number in the range 0 ≤ ? ≤ 1). The joint...