particle in a box is in three different states Ψ1=A1e(-y^2)/(4) Ψ2=A2e(-y^2)/(4) Ψ3=A3e(-y^2)/(4) .(a)....NORMALIZE these states in...
particle in a box is in three different states
Ψ1=A1e(-y^2)/(4)
Ψ2=A2e(-y^2)/(4)
Ψ3=A3e(-y^2)/(4)
.(a)....NORMALIZE these states in interval (-infinity to + infinity) ?
(b)....is the probability of finding the particle in interval 0<y<1 when particle is in states Ψ3 .?
(c)....is the same sum of the separate probabilities for states Ψ1 and Ψ2.?
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particle in a box is in three different states
Ψ1=A1e(-y^2)/(4)
Ψ2=A2e(-y^2)/(4)
Ψ3=A3e(-y^2)/(4)
.(a)....NORMALIZE these states in...
PROBLEMS 2.32 The wavefunction for a particle in one dimension is given by Another state that...
PROBLEMS 2.32 The wavefunction for a particle in one dimension is given by Another state that the particle may be in is A third state the particle may be in is y2/4 Normalize all three states in the interval-oo < y <-co (i.e., find A1,A2, and A3) is the probability of finding the particle in the interval 0 y < 1 when the particle : is in the state vs the same as the sum of the separate probabilities for...
8. A particle in a box (0x<L) has wave functions and energies of En 8m2 a)...
8. A particle in a box (0x<L) has wave functions and energies of En 8m2 a) Normalize the wave functions to determine A b) At t-0, ψ(x)-vsv, + ψ2 . 2. c) The particle will oscillate back and forth. Derive an expression for the oscilla- tion frequency in terms of h, m, and L Derive expressions for Ψ(x, t) and |Ψ(x, t)
for a particle in a one dimensional box of length L if the particle is on...
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
help Part B. Open questions. 1. (30 points) For the one-dimensional particle in a box of...
help
Part B. Open questions. 1. (30 points) For the one-dimensional particle in a box of length L. a. Write the wavefunction for the fifth excited state b. Calculate the energy for the fifth excited state when L = 18 and m = Ing. c. Write an integral expression for the probability of finding the particle between L/4 and L/2, for the second excited state. d. Calculate the numerical probability of finding the particle between 0 and L15, for the...
A particle of charge q and mass m is bound in the ground state of a one-dimensional harmonic osci...
A particle of charge q and mass m is bound in the ground state of a one-dimensional harmonic oscillator potential with frequency oo. At time t-0 a weak spatially uniform electric field (E) is turned on, so that the perturbation to the Hamiltonian can be described as R'(t) =-q Exe-t/t for t> 0. Using first order, time-dependent perturbation theory, calculate the following probabilities: (a) the particle is detected in the first excited state after a very long time (t »...
please help 1. The eigenfunctions of a particle in a square two-dimensional box with side lengths...
please help
1. The eigenfunctions of a particle in a square two-dimensional box with side lengths a = b = L are non, (x, y) = { sin ("T") sin (9,7%) = xn, (x)}n, (y) where n. (c) and on, (y) are one-dimensional particle-in-a-box wave functions in the x and y directions. a. Suppose we prepare the particle in such a way that it has a wave function V (2,y) given by 26,0) = Võru (s. 1) + Vedra ....
a) Show that the n=1 and n=2 states of the particle-in-a-box are orthogonal. b) Show that...
a) Show that the n=1 and n=2 states of the particle-in-a-box are orthogonal. b) Show that the n= 0 and n= 1 states of the harmonic oscillator are orthogonal. c) Show that the 1s and 2s states of the hydrogen atom are orthogonal.
Particle in a box Figure 1 is an illustration of the concept of a particle in...
Particle in a box Figure 1 is an illustration of the concept of a particle in a box. V=00 V=00 V=0 Figure 1. A representation of a particle in a box, where the potential energy, V, is zero between x = 0 and x = L and rises abruptly to infinity at the walls. The Schrödinger equation for a particle in a box reads t² d²u Y +V(x)y = Ey 2m dx2 + (1) where ħ=h/21 , y represents the...
Find the definite integral that is equal to the probability of finding the particle between: a)...
Find the definite integral that is equal to the probability of
finding the particle between:
a) x=0 and x=25
b)x=25 and x=50
When described by the normalized wave function 4
4 (particle in a box n = 1) 5 (particle in a box n = 2) 6 (particle in a box n = 3)
A box contains five coins. For each coin there is a different probability that a head...
A box contains five coins. For each coin there is a different probability that a head will be obtained when the coin is tossed. (Some of the coins are not fair coins!) Let pi denote the probability of a head when the i th coin is tossed (i = 1, . . . , 5), and suppose that p1 = 0, p2 =1/4, p3 =1/2, p4 =3/4, p5 =1. The experiment we are interested in consists in selecting at random...
PROBLEMS 2.32 The wavefunction for a particle in one dimension is given by Another state that the particle may be in is A third state the particle may be in is y2/4 Normalize all three states in the interval-oo < y <-co (i.e., find A1,A2, and A3) is the probability of finding the particle in the interval 0 y < 1 when the particle : is in the state vs the same as the sum of the separate probabilities for...
8. A particle in a box (0x<L) has wave functions and energies of En 8m2 a) Normalize the wave functions to determine A b) At t-0, ψ(x)-vsv, + ψ2 . 2. c) The particle will oscillate back and forth. Derive an expression for the oscilla- tion frequency in terms of h, m, and L Derive expressions for Ψ(x, t) and |Ψ(x, t)
help
Part B. Open questions. 1. (30 points) For the one-dimensional particle in a box of length L. a. Write the wavefunction for the fifth excited state b. Calculate the energy for the fifth excited state when L = 18 and m = Ing. c. Write an integral expression for the probability of finding the particle between L/4 and L/2, for the second excited state. d. Calculate the numerical probability of finding the particle between 0 and L15, for the...
A particle of charge q and mass m is bound in the ground state of a one-dimensional harmonic oscillator potential with frequency oo. At time t-0 a weak spatially uniform electric field (E) is turned on, so that the perturbation to the Hamiltonian can be described as R'(t) =-q Exe-t/t for t> 0. Using first order, time-dependent perturbation theory, calculate the following probabilities: (a) the particle is detected in the first excited state after a very long time (t »...
please help
1. The eigenfunctions of a particle in a square two-dimensional box with side lengths a = b = L are non, (x, y) = { sin ("T") sin (9,7%) = xn, (x)}n, (y) where n. (c) and on, (y) are one-dimensional particle-in-a-box wave functions in the x and y directions. a. Suppose we prepare the particle in such a way that it has a wave function V (2,y) given by 26,0) = Võru (s. 1) + Vedra ....
a) Show that the n=1 and n=2 states of the particle-in-a-box are orthogonal. b) Show that the n= 0 and n= 1 states of the harmonic oscillator are orthogonal. c) Show that the 1s and 2s states of the hydrogen atom are orthogonal.
Particle in a box Figure 1 is an illustration of the concept of a particle in a box. V=00 V=00 V=0 Figure 1. A representation of a particle in a box, where the potential energy, V, is zero between x = 0 and x = L and rises abruptly to infinity at the walls. The Schrödinger equation for a particle in a box reads t² d²u Y +V(x)y = Ey 2m dx2 + (1) where ħ=h/21 , y represents the...
Find the definite integral that is equal to the probability of
finding the particle between:
a) x=0 and x=25
b)x=25 and x=50
When described by the normalized wave function 4
4 (particle in a box n = 1) 5 (particle in a box n = 2) 6 (particle in a box n = 3)
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