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(3) A particle has the following unnormalized wave function et (a is a constant) in 3-...
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a...
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a ψ(x,0) = 0 otherwise where A, a, and b are constants. a) Normalize ψ(x,0). b) Draw (x,0). c) Where is the particle most likely to be found at t-0? d) What is the probability of finding the particle to the left of a? e) What is the expectation value of x?
A quantum object confined to a container of dimension a is described by this unnormalized wave...
A quantum object confined to a container of dimension a is described by this unnormalized wave function: this wave function Phi(x)n = A(1-x/a) where A is the normalization constant. Given that 0 ≤ x ≤ a, what is the value of the constant A?
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimens...
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimension x is given by the following expression: x <0,x>2L (A) Determine the value of the normalization constant c. (B) Draw the wavefunction. (C) Calculate Prob(L/2 S x 3 3L/2), the probability of finding the particle between x - L/2 and 3L/2
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimension x is given by the following expression:...
A particle moving in one dimension is described by the wave function ...
A particle moving in one dimension is described by the wave function$$ \psi(x)=\left\{\begin{array}{ll} A e^{-\alpha x}, & x \geq 0 \\ B e^{\alpha x}, & x<0 \end{array}\right. $$where \(\alpha=4.00 \mathrm{~m}^{-1}\). (a) Determine the constants \(A\) and \(B\) so that the wave function is continuous and normalized. (b) Calculate the probability of finding the particle in each of the following regions: (i) within \(0.10 \mathrm{~m}\) of the origin, (ii) on the left side of the origin.
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscill
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscillator, respectively. (a) Normalize (r, 0). (b) Find the wavefunction (r, t) at a later time t and hence evaluate (x, t) 2. Leave your answers involving expressions in to and ₁. c) sing the following normalized expression of...
The wave function given below is suggested to fit the particle in a box of length...
The wave function given below is suggested to fit the particle in a box of length L in one dimension: Duh!! also known as the particle on a line: V=N (L x-); where N is the normalization constant. Problem One. List three conditions (in a short phrase) that make any wavefunction acceptable. For each condition, show that the above wavefunction satisfies the condition you listed. (Use the allotted spaces below to answer the question). (1) (III).
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x)...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...
Consider a particle confined to one dimension and positive r with the wave function 0, z<0...
Consider a particle confined to one dimension and positive r with the wave function 0, z<0 where N is a real normalization constant and o is a real positive constant with units of (length)-1. For the following, express your answers in terms of a: a) Calculate the momentum space wave function. b) Verify that the momentum space wave function is normalized such that (2.4) c) Use the momentum space wave function to calculate the expectation value (p) via (2.5)
The lowest energy unnormalized wave function of H molecule is (ri and r2 the distances between...
The lowest energy unnormalized wave function of H molecule is (ri and r2 the distances between the electron and nuclei 1 and 2, respectively) 1. ф 3D (е-i/ao +e-ra/ao) 2. ф %3D (е-r/ao — е-ra/ao) 3. ф3D е-n/ao 4. p = e2/ao
The lowest energy unnormalized wave function of H molecule is (ri and r2 the distances between the electron and nuclei 1 and 2, respectively) 1. ф 3D (е-i/ao +e-ra/ao) 2. ф %3D (е-r/ao — е-ra/ao) 3. ф3D е-n/ao...
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...
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a ψ(x,0) = 0 otherwise where A, a, and b are constants. a) Normalize ψ(x,0). b) Draw (x,0). c) Where is the particle most likely to be found at t-0? d) What is the probability of finding the particle to the left of a? e) What is the expectation value of x?
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimension x is given by the following expression: x <0,x>2L (A) Determine the value of the normalization constant c. (B) Draw the wavefunction. (C) Calculate Prob(L/2 S x 3 3L/2), the probability of finding the particle between x - L/2 and 3L/2
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimension x is given by the following expression:...
The wave function given below is suggested to fit the particle in a box of length L in one dimension: Duh!! also known as the particle on a line: V=N (L x-); where N is the normalization constant. Problem One. List three conditions (in a short phrase) that make any wavefunction acceptable. For each condition, show that the above wavefunction satisfies the condition you listed. (Use the allotted spaces below to answer the question). (1) (III).
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...
Consider a particle confined to one dimension and positive r with the wave function 0, z<0 where N is a real normalization constant and o is a real positive constant with units of (length)-1. For the following, express your answers in terms of a: a) Calculate the momentum space wave function. b) Verify that the momentum space wave function is normalized such that (2.4) c) Use the momentum space wave function to calculate the expectation value (p) via (2.5)
The lowest energy unnormalized wave function of H molecule is (ri and r2 the distances between the electron and nuclei 1 and 2, respectively) 1. ф 3D (е-i/ao +e-ra/ao) 2. ф %3D (е-r/ao — е-ra/ao) 3. ф3D е-n/ao 4. p = e2/ao
The lowest energy unnormalized wave function of H molecule is (ri and r2 the distances between the electron and nuclei 1 and 2, respectively) 1. ф 3D (е-i/ao +e-ra/ao) 2. ф %3D (е-r/ao — е-ra/ao) 3. ф3D е-n/ao...
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...
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