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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_forwardConsider a 1D particle in a box confined between a = 0 and x = 3. The Hamiltonian for the particle inside the box is simply given by Ĥ . Consider the following normalized wavefunction 2m dz² ¥(2) = 35 (x³ – 9x). Find the expectation value for the energy of the particle inside the box. Give your 5832 final answer for the expectation value in units of (NOTE: h, not hbar!). In your work, compare the expectation value to the lowest energy state of the 1D particle in a box and comment on how the expectation value you calculated for the wavefunction ¥(x) is an example of the variational principle.arrow_forward
- 8. Do the linear momentum operator px and angular momentum operator Lx commute. Can the velocity in the x direction (vx) and angular momentum in the x direction (Lx) be measured simultaneously to an arbitrary precision?arrow_forward8a. What is the expectation value of the linear momentum for the 1-D wavefunction: -ax 2 (x) = Ne where -0arrow_forwardWhere are the nodes in the wavefunction for a particle confined to a box with 0 < x < a and n=3?arrow_forwardConsider again the system in quizzes 1 and 2, namely a particle moving in one dimension described by the normalized wavefunction (x) = 30 1 (а — х) for 0 a . а Determine the expectation value () for the particle.arrow_forwardWhat is the kinetic energy of a particle described by the wavefunction cos(kx)? ħ² d² 2m dx² KEarrow_forwardThe rotation of a molecule can be represented by the motion of a particle moving over the surface of a sphere with angular momentum quantum number l = 2. Calculate the magnitude of its angular momentum and the possible components of the angular momentum along the z-axis. Express your results as multiples of ℏ.arrow_forwardConsider a single particle with rest mass m residing in a one-dimensional space, x. This particle experiences a potential energy V(x) = ∞ for x a, and a potential energy V(x) = 0 for 0 < x < a. The solutions to the Schrödinger Equation for this system are 12. 2 Vn(x) : sin a where n is the state's quantum number. Show that the ground state wave function is normalized.arrow_forwardA particle freely moving in one dimension x with 0 ≤ x ≤ ∞ is in a state described by the normalized wavefunction ψ(x) = a1/2e–ax/2, where a is a constant. Evaluate the expectation value of the position operator.arrow_forwardImagine a particle free to move in the x direction. Which of the following wavefunctions would be acceptable for such a particle? In each case, give your reasons for accepting or rejecting each function. (1) Þ(x) = x²; (iv) y(x) = x 5. (ii) ¥(x) = ; (v) (x) = e-* ; (iii) µ(x) = e-x²; (vi) p(x) = sinxarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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