Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x)...
The wave function of a restricted particle on the x-axis is between x = 0 and x = 1 ψ= ax ^2 and everywhere else ψ = 0. a) Find the value of constant a b) Find the probability that the particle is between x = 0.1 and x = 0.2 c) Find the wait value for the position of the particle
II.6. The wave function of a particle in a 1D rigid box (infinite potential well) of length L is: v, 8, 1) = sin(x)e-En/5). n = 1,2,3... What is the probability density of finding the particle in its 2nd excited state?
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a ψ(x,0) = 0 otherwise where A, a, and b are constants. a) Normalize ψ(x,0). b) Draw (x,0). c) Where is the particle most likely to be found at t-0? d) What is the probability of finding the particle to the left of a? e) What is the expectation value of x?
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.
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...
A particle moving in one dimension is described by the wave function$$ \psi(x)=\left\{\begin{array}{ll} A e^{-\alpha x}, & x \geq 0 \\ B e^{\alpha x}, & x<0 \end{array}\right. $$where \(\alpha=4.00 \mathrm{~m}^{-1}\). (a) Determine the constants \(A\) and \(B\) so that the wave function is continuous and normalized. (b) Calculate the probability of finding the particle in each of the following regions: (i) within \(0.10 \mathrm{~m}\) of the origin, (ii) on the left side of the origin.
22. (20 points) The wave function of an electron that is confined to the sam (x) = be-\x[/2 nm a. (5 points) Qualitatively sketch the wave function as a function of po the value b on the plot. unction as a function of position and mark the location of b. (10 points) Find the value of b. c. (5 points) What is the probability of finding the electron in a 0.010 nm-wide region centered at 1.0 nm?
Please include explanations I. The graph shows the wave function ψ(x) of a particle between x =0 nm and x-2.0 nm. The cvx 0to 2.0 nm probability is zero outside of this region. In other words,p(x) - a) Find c, as defined by the figure. P(x) b) What is the probability of finding a particle between 1.0 nm and 2.0 nm? c) What is the smallest range of velocities you could find for an electron confined to this distance of...
A particle is represented by the following wave function: ψ(x) =0 x<−1/2 ψ(x) =C(2x + 1) −1/2 < x < 0 ψ(x) =C(−2x + 1) 0 < x < +1/2 ψ(x) =0 x > +1/2 (a)Evaluate the probability to find the particle between x=0.19 and x=0.35. (b) Find the average values of x and x2, and the uncertainty of x: Δx=√(x2)av-(xav)2 xav= (x2)av= Δx =
5. The function x< 0 0 < x < a ψ(x)-Ax(1-(x/a)] is an acceptable wavefunction for a particle in a one-dimensional space (x can take values between -oo and +oo) (a) Give two reasons why this is an acceptable wave function. (b) Calculate the normalization constant A. (c) Using the definition for the average of an observable "o" described by the operator "o": and to)