5. A microscopic oscillator has its first and second excited states 0.05 eV and 0.10 eV above the ground-state energy. Calculate the Boltzmann factor for the ground state, first excited state, and second excited state, at room temperature.
Q: 3. Use the WKB approximation to find the energy level of a particle moving in the potential: V(x) =…
A: Solution by image is shown belowExplanation:Step 1: Step 2: Step 3: Step 4:
Q: Q5: Imagine a particle that can be in only three states, with energies -0.05 eV, 0 eV, and 0.05 eV.…
A:
Q: 6. One electron is trapped in a one-dimensional square well potential with infinitely high sides.…
A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…
Q: Imagine a certain kind of particle, such that each single-particle state can be occupied by at most…
A: Red
Q: If the wave function has the following equation y = 4cosA + 4isinA a. Determine the conjugate…
A: Conjugate of Complex Number: Two complex numbers which differ only in the sign of imaginary parts…
Q: Ignoring the fine structure splitting, hyperfine structure splitting, etc., such that energy levels…
A: Energy levels of a singly ionized He atom(Z=2) is given by En=-Z2n2×13.6=-22n2×13.6 eV Hence from…
Q: If I have three fermions in states v, y', and " (a) Construct a fully asymmetric state V (F1, 72,…
A:
Q: 1. Derive the density of states as a function of energy for a purely two-dimensional electron…
A:
Q: a) Describe the Variational Principle b) The variation method is applied to a harmonic oscillator…
A: Variational principle or variational method is used for evaluating the energies of the ground state.…
Q: For what time-intependent potential energy function V(r) does Y satisfy the Schrödinger equation for…
A:
Q: 2. A free particle is described by the wave function V(x, t) = A exp [i ((2.16 × 10¹² m¯¹)x − (3.45…
A:
Q: Two copper nanowires are insulated by a copper oxide nano-layer that provides a 10.0-eV potential…
A: Given: Potential barrier V=10.0 eV To find: 1) Tunneling probability between nanowires by 7.00 eV…
Q: 1. Compute the partition function Z¡(T, V, N, B) of a single molecule as a function of the…
A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…
Q: a.Draw the wave function for a particle in a box at the n-3 energy level. b.Draw the probability…
A:
Q: In the Bohr model, the radii of the ground and first excited state orbits are ao and 4ao,…
A: The ground state wave function of H atom isThe probability of finding the electron when the atom is…
Q: harmonic oscillator with energy levels ε is in equilibrium with a reservoir at temperature T.…
A:
Q: 2033 Consider a system of No non-interacting quantum mechanical oscilla- tors in equilibrium at…
A: Given, A system of N non-interacting quantum mechanical oscillator in equilibrium at temperature T.…
Q: C. For a particle of mass 9.10938356×10-31 kg scooting back and forth on a wire of length 13×10-10…
A:
Q: 2- There is a system consisting of N independent particles. Each particle can have only one of the…
A: We have N independent particles existing in two energy levels Eo and -Eo. Let number of particles in…
Q: 1. A model of interest for quantum mechanics, due to its simplicity, corresponds to a delta wall. A…
A: Given, Potential is Vx=δx width of the well is L and height o the well is SL And Schrodinger's…
Q: 6. Consider an electron in a hydrogen atom in a state given by Y(t = 0) = = {D311 (1,0,0) + 20 310…
A: Given that, the state of an electron in the hydrogen atom is Ψt=0=15Φ311r,θ,φ+2Φ310r,θ,φ To find a)…
Q: 1. Consider the normal Zeeman effect applied to the 3d to 2p transition. Sketch an energy-level…
A: Given Consider the normal Zeeman effect applied to the 3d to 2p transition. Sketch an energy-level…
Q: 2. A particle is in the second excited state of an infinite cubic potential well of side a.…
A:
Q: 3. Certain surface waves in a fluid travel with phase velocity v(b/2), where b is a constant. Find…
A: We have surface waves in a fluid which travel with a phase velocity vp=b/λ where λ is the…
Q: An electron is trapped in an infinitely deep potential well 0.300 nm in width. a. If the electron is…
A:
Q: Which of the following wave functions can be taken as a probability density? a. y(x)=sin(x) b. w(x)…
A:
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
- 1. A particle in an infinite well is in the ground state with energy 1.54 eV. How much energy must be added to reach the second excited state (n = 3)? The third excited state (n = 4)? 2. An electron is trapped in a one-dimensional well of width 0.132 nm. The electron is in the n = 10 state. What is the energy of the electron? What is the uncertainty in its momentum?According to the quantum mechanical postulates, the following graph shows: V(x) y(x) (a) (c) OA. One well behaved and acceptable wave function. B. Two well behaved and acceptable wave functions. OC. Two unacceptable wave functions. D. Four unacceptable wave functions. y(x) (b) pů u V(x)17. Four quantum particles with energy E approach a potential energy barrier from the left. Each has a probability for tunneling through the barrier. Rank in order, from largest to smallest, the tunneling probabilities (Ptunnel)1 to (Ptunnel)4. E E E E 1 eV 2 eV 1 eV 2 eV 2w 0.5w Barrier 1 Barrier 2 Barrier 3 Barrier 4 Order: Explanation:
- 4. Consider two indistinguishable spin-1/2 fermions in a one-dimensional infinite square well of length L. Construct the state vector and determine the energy for the ground-state of the two-particle system assuming the particles are non-interacting. i. ii. Determine the first excited state energy of the two-particle system and give all its state vectors, again assuming the particles are non-interacting. What is the degeneracy of the first excited state? ji. Suppose the particles interact via the potential V(x, x2) = k(x1 – x2)² where k is positive and small. Discuss quantitatively how the ground and first-excited state energies differ from the case for non-interacting particles. 5. A one-electron atom has atomic number Z, mass number M and a spherical nucleus of radius ry. Assume electric charge +Ze is uniformly distributed throughout the volume of the nucleus. Ignoring spin, use first order non-degenerate perturbation theory and the hydrogenic wave functions adapted to the…4. The first excited state of the helium atom lies at an energy 19.82 eV above the ground state. If this excited state is three-fold degenerate while the ground state is non-degenerate, find the relative populations of the first exited and the ground states for helium gas in thermal equilibrium at 10,000 K.1. Particle in a Box. A particle of mass m that is confined in a one- dimensional box of length L, i.e. x € (0, L), is described by the wave function: (x, t) = A sin where En = nnx L expli- n²π²ħ² 2m [², Ent ħ where n E N where n E N. The wave function is zero outside the box. Calculate the normalization constant A and compute the uncertainty of position and momentum regardless of the quantum number n.
- 2. Suppose a particle of mass, m, has energy E, and wave function: WE (x, t = 0) = Aeikx + Be-ikx What is WE(x, t)? Calculate the probability density of the particle when it has the wavefunction, E (x, t). If you wish to simply your answer algebraically, use this information: let A = aeia and B = beif and A = a - B. where the variables a, b, a, ß are all real! WARNING: Simplifying the equation is somewhat time consuming. Show/explain why p(x,t) is not normalizable. According to quantum theory, all physical systems must have an associated wavefunction that is normalizable. Explain why plane wave solutions to Schrodinger's equation are used in quantum theory, despite not being normalizable?1. A particle moving in the positive x-direction encounters a finite step-function potential of magnitude V, at x = 0 as illustrated. a. b. The energy of the particle is E > Vo- I. ii. III. iii. PHYS 2305 Homework 7 II. iii. The energy of the particle is E 0). Identify terms as Pincident, reflected and transmitted- Apply boundary conditions to determine relationships between the wavefunction coefficients. Determine P(T) the probability of transmission and P(R) the probability of reflection for the particle. Write the wavefunction for the particle in region 1 (x 0). Identify terms as incident, reflected and transmitted- Apply boundary conditions to determine relationships between the wavefunction coefficients. Determine P(T) the probability of transmission and P(R) the probability of reflection for the particle. X6. The Aharonov-Bohm effect is strong evidence that the vector potential A and scalar potential V are fundamental rather than B and E. In other words, the properties of a particle can be effected by changes in A or V, even if B and E remain constant and zero. Give an exact example where A changes but Band jare unaffected. You can be as cute or as boring as you like with this one. ☺
- 2. An electron is confined to a nanowire 2 nm in length. Model this system as a 1-D particle-in-a-box, going from 0 to 2 nm. a. Compute the probability that the electron is in the range 0.95 ≤ x ≤ 1.05 nm for the states n = 1, 2, 3. b. Compute the probability that the electron is located within a distance of 0.05 nm of the left end of the wire for each of the states n = 1, 10, 100.1. Use the I function to do the following: TZ (a) prove that z!(-z)! : where z is any real number sin(TZ1. 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.