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Assume that for a particle on a ring the operator for the
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Physical Chemistry
- What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?arrow_forwardIndicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue. a ddxcos4xb d2dx2cos4x c px(sin2x3)d x(2asin2xa) e 3(4lnx2), where 3=3f ddsincos g d2d2sincosh ddtanarrow_forwardA possible wavefunction for an electron in a region of length L is sin(3πx/L). Normalize this wavefunction (to 1).arrow_forward
- (a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0xa/4.(b) Calculate this probability for n=1,2, and 3.arrow_forwardFor a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0 xa/4. (b) Calculate this probability for n = 1, 2, and 3arrow_forwardFor the system described in Exercise E7B.1(a) (A possible wavefunction for an electron in a region of length L (i.e. from x = 0 to x = L) is sin(2πx/L). Normalize this wavefunction (to 1)), what is the probability of finding the electron between x = L/4 and x = L/2?arrow_forward
- The speed of a certain proton is 0.45 Mm s−1. If the uncertainty in its momentum is to be reduced to 0.0100 per cent, what uncertainty in its location must be tolerated?arrow_forwardConsider an isotropic three-dimensional harmonic oscillator for a particle of mass "m" and the Hamiltonian H=P2/2m + m(w0)2R/2 Where P and R are the three-dimensional momentum and position operators w0 angular frequency. Find the eigenvalues and the eigenfunctions of the Hamiltonian and the degrees of degeneracy for the energy levels.arrow_forwardWhat is the eigenvalue for the eigenfunction e^(3√3ix) ?arrow_forward
- What values of J may occur in the terms (i) 3D, (ii) 4D, (iii) 2G? How many states (distinguished by the quantum number MJ) belong to each level?arrow_forward(a) What are the possible values for mℓ when the principal quantum number (n) is 2 and the angular momentum quantum number (ℓ) is 0? (b) What are the possible values for mℓ when the principal quantum number (n) is 3 and the angular momentum quantum number (ℓ) is 2?arrow_forward
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