4. Which of the functions satisfy the boundary conditions for a particle in the one-dimensional box shown below? V(w) O COS 2X a. cos b. sin RX 2a c. x (a-x) d. All are correct

Is the function w(x) = sinx an eigenfunction for the linear momentum operator, 6.? If yes, what is the eigenvalue? O Yes, the eigenvalue is -1 Yes, the eigenvalue is sinx O Yes, the eigenvalue is – in O No

Normalize the wave function e-ax in the range 0≤x≤ ∞, with a > 0.

Physical Chemistry.   Explain the origin of quantization of translational motion. Write an equation for the energy of a particle and state two information you get from the equation.

4. Given these operators A=d/dx and B=x², can you measure the expectation values of the corresponding observables to infinite precision simultaneously?

1 For a particle in a one dimensional square well in which the potential energy rises to a finite value V at each end, and zero inside the well, show that for any V and L there is at least one bound state.

Do the kinetic energy operator and momentum operator commute once they are applied on f(x) =AX? Select one: O a. Yes they do commute O b. They don't commute O c. No clear conclusion could be drawn O d. None

a. Find the average position on the x-axis, , for the wavefunction of a 2D particle in a box where sin ( sin () 3TTX- ¥32 =