Question
HOMEWORK: REPRESENTATIONS OF WAVE FUNCTIONS QM Hw-1 Name 1 Recall the quantum state for a particle in the infinite square well Re(p)) 14,)-ti40+|rlus) |w,). from the tutorial. A different Ip) v6 visual representation of this state is shown at right. (Note: solid-.. ·T+R, T-. lines represent real parts while dashed lines represent imaginary parts.) a. The graph at right is a momentium-space wave function. Explain why this name is appropriate What are the units for the vertical axis? Is your answer consistent with the overall normalization of the state? Explain. b. How do these units compare to the units for the position-space wave function? Describe how you wouid determine the probability of finding the momentum within a range from p = p,to p = p c. d. Suppose you were given only the momentum-space wave function for a particle, (p). Is it possible to determine the probability of the outcome of an energy measurement? Explain. i. ii. Is it possible to determine the probability of the outcome of a position measurement? Explain. Tutorials in Physics: Quantum Mechanics Heron, Shaffer, and PEG U W Preliminary First Edition, 2017
Explanation / Answer
To represent wavefunction, we need a basis, it could be represented in position basis or in momentum basis or any other dynamical quantity may be used. So, Its appropriate.
Vertical axis represents wavefunction,which itself has no physical significance, and its square gives propability which itself has no unit...therefore vertical axis has no unit.
Wavefunctions in either basis are Fourier Transforms/inverse transforms of each other.
Integrating from p1 to p2, mod square of wavefunction, gives probability of finding the particle between p1 and p2 range.
