Calculate the uncertainties dr = V(r2) and dp = Vp?) for a particle confined in the region -a < x < a. The wave function of the particle is: 1 = (x) 2a -a < r < a, COS (x) = 0, I > a, r < -a.
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As we can see the given wave function is normalised and in outside region it's zero. Therefore
This is the position uncertainty.
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- 6QM Please answer question throughly and detailed.For a quantum particle in a scattering state as it interacts a certain potential, the general expressions for the transmission and reflection coefficients are given by T = Jtrans Jinc R = | Jref Jinc (1) where Jinc, Jref, Jtrans are probability currents corresponding to the incident, reflected, and transmitted plane waves, respectively. (a). potential For the particle incident from the left to the symmetric finite square well -Vo; a < x < a, V(x) = 0 ; elsewhere, show that B Ꭲ ; R = A AA particle with mass m is in the state mx +iat 2h V (x, t) = Ae where A and a are positive real constants. Calculate the expectation value of (p).
- The wave function W(x,t)=Ax^4 where A is a constant. If the particle in the box W is normalized. W(x)=Ax^4 (A x squared), for 0<=x<=1, and W(x) = 0 anywhere. A is a constant. Calculate the probability of getting a particle for the range x1 = 0 to x2 = 1/3 a. 1 × 10^-5 b. 2 × 10^-5 c. 3 × 10^-5 d. 4 × 10^-5An electron with an initial kinetic energy of 1.542 eV (in a region with 1.095 eV potential energy) is incident on a potential step (extending from x=0 to ∞) to V=2.381 eV. What is the transmission probability (in %)? FYI: If we had a travelling wave arriving at a similar potential DROP, then k1 (for x<0) would be real and the symmetry of R=(k1-k2)2/(k1+k2)2 implies reflection/transmission are the same as a potential RISE with the same energies but k1 and k2 swapped.A particle with mass m is in the state .2 mx +iat 2h Y(x,t) = Ae where A and a are positive real constants. Calculate the expectation values of (x).
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