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Assume that for a particle on a ring the operator for the
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Student Solutions Manual for Ball's Physical Chemistry, 2nd
- Indicate 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_forward8. 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_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_forward
- The 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_forward5arrow_forward
- Imagine 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_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_forwardA normalized wavefunction for a particle confined between 0 and L in the x direction is ψ = (2/L)1/2 sin(πx/L). Suppose that L = 10.0 nm. Calculate the probability that the particle is (a) between x = 4.95 nm and 5.05 nm, (b) between x = 1.95 nm and 2.05 nm, (c) between x = 9.90 nm and 10.00 nm, (d) between x = 5.00 nm and 10.00 nm.arrow_forward
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