A particle is trapped in an infinite potential energy well. It is in the state with quantum number n = 14. How many maxima does the probability density have? A. none В. 7 С. 13 D. 14 Е. 15
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- Define the quantum numbers n, l, ml , s , and ms .wave function Find the anplitude A of the above =xp(品). %31 7. 77 UIS יר 11 Sin 7. 7. UIS o(x)=A sin (ax) free particle - having particle Electron can be considered a s and Wave function int, Well Hn electron trapConsider the Bloch sphere for a single qubit. What is the state represented by the Bloch vector (-1,0,0)? (12+) - i|z_)) a. b. |z_) c. (z+) d. • e. (12+)+ 12-)) (12+) - 12-))
- A quantum mechanical particle moving in one dimension between impenetrable barriers has energy levels ϵ,4ϵ,9ϵ,...ϵ, 4ϵ, 9ϵ, ... , that is En=ϵn2En=ϵ n2 . Suppose that ϵ=0.035eVϵ =0.035 eV for a certain such quantum system. What is the probability (as a percent) that such a system will be in its ground state when it is in contact with a reservoir at room temperature? The probability that the system will be in its ground state when it is in contact with a reservoir at room temperature is1. A particle is confined to the x-axis between x = 0 and x = L. The wave function 3π of the particle is = A sin (²x) + A sin (37 x) with A E R. 4 2L a. b. C. Determine A. Determine the probability that the particle is in the interval [0,1]. J Determine (x).