calculate the expectation value of position x for a particle in a box of length L in the state n=1
calculate the expectation value of position x for a particle in a box of length L...
fer pourice 5. Calculate the ground state expectation values for position, <x>, and momentum <p> for a particle confined by an infinite potential (in a box). Do your answers make sense? ψ( ( ) 1,2,3 Ψ( | 1 x)- Asin Jor n= ,
The answer is attached for reference HW15.3 A particle in a box of length L is in its ground state (n 1). The wall of the box is suddenly moved outward to x-2L. Calculate the probability that the particle will be found in the ground state of the expanded box. Determine the state of the expanded box most likely to be occupied by the particle.
for a particle in a one dimensional box of length L if the particle is on the n=4 state what is the probability of finding the particle within a) 0<x<5L/6 b) L/4<x<L/2 c) 5L/6<x<L
Calculate the expectation value of the kinetic energy for the particle of mass m on a line of length a in a state with quantum number n. Compare your result to the expression for the energy level of the particle and explain any similarities or differences.
A particle is in the ground state of a box of length L (from -L/2 to L/2). Suddenly the box expands symmetrically to twice its size (from -L to L), leaving the wave function undisturbed. Show that the probability of finding the particle in the ground state of the new box is (8/3pi)^2.
64 Consider a particle in a one-dimensional box in the ground state v, and the first excited state , described by the wave functions listed below. For each wave function, calculate the expec- tation value of the position (x), the expectation value of the position squared (), the expecta- tion value of the momentum (p), and the expectation value of the momentum squared (p2). 2 . 2x Ossa 0sxSa (b) Y2(x) = Vasin-
For a one-dimensional particle in a box system of length L (infinite potential well) with 2/L sin (nnx)/L where n= 1,2,3.. b(x) at which n value(s) the probability of finding the particle is the highest at L/2? a(x) 3(x) 2(x) (x) L
Consider a particle in a box of length L-1 in a state defined by the wavefunction,
for a one dimensional particle in a box, write an integral expression for the average value, or expectation value, of the momentum of the n=1 state
For the one-dimensional particle in a box of length L = 1 Å, what will be the energy of the ground state? a. Write Schrodinger’s equation for if the potential between 0 and L is zero b. Write Schrodinger’s equation for if the potential between 0 and L has a constant value of V_o