1. By providing step by step computations, show that the effect of the following quantum circuit is to interchange the state of two qubits (a, b). Provide the corresponding 4 x 4 matrix of the circuit.
Q: What is the value of quantum number, n, for a 1-dimensional particle-in-a-box system in which the…
A: ψ=23πsin(2x3) is the normalized wavefunction.
Q: 3. In the potential barrier problem, if the barrier is from x-aa, E a region? (k²: 2mE > 0) ħ² Ans:
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Q: 4. Show that the canonical ensemble probability 1 P. = e`BE Z follows from maximizing S = -k>p, In…
A: Canonical ensemble: In canonical ensemble, temperature, volume, and a number of the particles of…
Q: 4. For free particle in a box (which is coupled to reservoir via the walls of the box), find using…
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Q: 3. Consider a particle in an infinite square well potential trapped between 0 < x < a. What is the…
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Q: 1. Solve the Schrodinger equation for a particle of mass, m, in a box. The box is modeled as an…
A: 1) Given: Length of the box is L. Potential inside the box is V0 Calculation: The schematic diagram…
Q: 3. Kittel, Ch2-3. Quantum harmonic oscillator. (a) Find the entropy of a set of N oscillators of…
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Q: 1. In a system of two conducting wires separated by a small distance L, an electron can potentially…
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Q: 4. Show that the canonical ensemble probability 1 P.=ラ follows from maximizing S = -kEp, In p,…
A: The canonical partition function is given as:
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A: A quantum circuit diagram typically looks like the following. The major components are. Quantum…
Q: Discuss the general properties of the eigenstates of the quantum harmonic oscillator.
A: The normalized wave function for the harmonic oscillator is given as, ψnx=mωh2nn!π12e-mωhx2Hnmωhx…
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Q: Sketch y and |p 2 for the n =4 and n = 5 states of a particle in a one-dimensional box.
A: Wavefunction A wavefunction is a mathematical function that encodes all the properties of a…
Q: 4. For parts a, b, c state whether the given wavefunction is admissible or not and justify your…
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Q: 1. Consider a 3D particle in a box with lengths a=2b=2c. a) Determine the combination of quantum…
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Q: 1. An electron is trapped in a region between two perfectly rigid walls (which can be regarded as…
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Q: 1. For the n 4 state of the finite square well potential, sketch: (a) the wave function (b) the…
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Q: 1. A particle of mass 2.00 x 10-10 kg is confined in a hollow cubical three-dimensional box, each…
A: Step 1:Answer 1:Step 2:Answer 2:Step 3:Answer 3:Step 4:Answer 4: From the probability distribution…
Q: Q4. Proof that the probability current for a wavefunction of the form (a) j = R(x)|² h ³s(x) m əx…
A: Since we answer up to one question, we will answer the first question only. Please resubmit and…
Q: 2. Suppose a particle of mass, m, has energy E, and wave function: WE(x,t = 0) = Aeik + Be-ik What…
A: Given: Mass of the particle =m Energy of the particle =E Wave function associated with the particle…
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- 4. Find the points of maximum and minimum probability density for the nth state of a particle in a one- dimensional box. Check your result for the n=2 state.2. A wave function is a linear combination of 1s, 2s, and 3s orbitals: y(r) = N(0.25 y,s + 0.50W2, +0.30W). Find the normalization constant N, knowing that 1s, 2s, and 3s orbitals are normalized.1. Given the following probability density function: p(x) = Ae¬^(x-a)². 2. A particle of mass, m, has the wavefunction given by: Þ(x,t) = Ce-a[(mx²/h) + it] . 3. In a few sentences, explain why it is impossible to calculate (p) in the first problem, whereas in the second problem this is straightforward. Highlight the key concepts that differentiate these problems.
- 3. Particle in a 2D Box. A quantum mechanical particle is confined in side a square 2D box, with side length L. Inside the box V=0 and outside the box V=infinity. Let the wave function to be (x,y). (a) write down the Schrodinger equation of (x,y). (b) Use the separation of variable method solve (x,y) (let the quantum numbers to be nx and ny.) (c) What is the energy for the state (nx, ny)? (d) What is the probability density p(x,y) for the state nx=3 and ny=3? Sketch this p(x,y) in a square.Chat gpt means downvoteConsider a particle in a 2-D box having Lx = 10 nm and Ly = 10 nm. a) Make a surface plot of all the wave functions for the first and second energy levels. b) What is the degeneracy of the second energy level? Compare and contrast the wave functions of the second energy level. c) How does the number of nodes in the x-coordinate change as n increases? How does the number of nodes in the y-coordinate change as n, increases? d) Explain whether or not those same states would be degenerate if Lx = 10 nm and Ly = 15 nm.