ikx 4 = ( 1 ) ₁4 4 = ( 1 ) ½s ihr = 2πTa find th expected value of momentum p if the particle function is : 2
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- classical physicsA Proton is confined to move in a one- dimensional bux of length 0.410 mm La) Find the lowest possible energy of the proton. Note: Answer must be in ev.A 4.90g Particle confined to a box of length L has a speed of 4.70mm/s a) lalhat is the classical Kinetic energy of Particle? the b) If the energy of the first excited State (n=2) is equal to the Kinetic energy found in part (a), what is the value Note: Answer must be in mi L? of c) Is the result found in part (b) realistic ? Explain.
- A hydhogen athm is m t's grand state cnzlD - Usmg Bohlite the orbit. the radiug Athe linea momentum Calanlate (a of the elechon the anfular momentum of the electron ( athe kinetic eneryy ethe putential energy ans O he folal energy.Estimate the lifetime of a state that gives rise to a line of width (a) 0.10 cm-1, (b) 1.0 cm-1, (c) 1.0 GHz.If an electron’s position can be measured to a precision of 15 nm, what is the uncertainty in its speed?Assuming the minimum speed must be at least equal to itsuncertainty, what is the electron’s minimum kinetic energy?
- When the position of a neutrino is measured, it has an uncertainty of 3.38 x 1018 meters. If the momentum is measured at the same time, calculate the minimum uncertainty in the momentum.What do we need to do to average over Θ and ф to get the probability that the electron is inside a shell of radius r and thickness dr?if th wavefunetion is: P (x) = AélxI a) calculate A so that Ycx) is normalızed b) calculate th wave function momentum space ocp)
- Determine the expectation values of the position (x) (p) and the momentum 4 ħ (x)= cos cot,(p): 5V2mw 4 mah 5V 2 sin cot 2 ħ moon (x)= sin cot, (p)= COS at 52mo 2 4 h 4 moh (x)= 52mo sin cot.(p) COS 2 h s cot, (p) 5V2mco 2 moh 5V 2 sin of as a function of time for a harmonic oscillator with its initial state ())))QUESTION 9 Consider the case of a 3-dimensional particle-in-a-box. Given: Y = V8 sin(3nx) sin(2ny) sin(4rz) What is the energy of the system? O 24h2/8m O sh?/8m O none are correct O 29h2/8m QUESTION 10 3 πχ sin sin () sin is a normalized wavefunction for the 3D particle-in-a-box. 1.5 O True O FalseI need the answer as soon as possible