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- 3. For free particles in two dimensions, what is density of states (DOS) in low speed limit (=p²/2m), and in high speed limit (=pc)?1. Given the following probability density function: p(x) = Ae¬^(x-a)². 2. A particle of mass, m, has the wavefunction given by: Þ(x,t) = Ce-a[(mx²/h) + it] . 3. In a few sentences, explain why it is impossible to calculate (p) in the first problem, whereas in the second problem this is straightforward. Highlight the key concepts that differentiate these problems.The infrared spectrum of 75Br19F consists of an intense line at 380. cm-1. Calculate its force constant, k, in units of N/m. (You can use the example as a sanity check.)
- neon (Ne) has in the same excited state: 18²282p30* 10 electrous. Fou create (Ne) atoms all p৮.dর हहा Hund's ruk apply to each energy level t the meon. eleitrons 1. calculate the spin , orbital and total anqular momenta of f a the cap) level oम (रंर) b. the (ad) fevel.4. Use the variational principle to estimate the ground state energy of a particle in the potential (∞0 x < 0 U(x) = \cx x≥0 Take xe-bx as a trial function.4. Normalize the following wavefunctions 4 55 (a) v(x) = sin (#2); =sin(); for a particle in a 1D box of length L. (b) (2) = xe-z|2 (c) (x) = e(x²/a²)+(ikz) 5. In a region of space, a particle with mass m and with zero energy has a time- independent wave-function (x) = Ae-2/12, where A and L are constants. Use your knowledge of the Schrödinger equation to determine the potential energy V(x) of the particle. Plot the potential function? What is the minimum potential energy for the particle, if it is an electron and L = 1 fm? Is this potential repulsive or attractive?