The Klein-Gordon equation V²y – m²ý = 0 describes the quantum-mechanics of relativistic spin-0 particles. Show that the solution for the function (F) in any volume V bounded by a surface S is unique if either Dirchlet or Neumann conditions are specified on S.
Q: Consider a spinless particle of mass, M which is moving in a 3-dimensional potential V(x, y, z) =…
A: Given: The potential of the particle moving in 3-dimensional well.
Q: Calculate the expectation value of p¹ in a stationary state of the hydrogen atom (Write p² in terms…
A: We are going to calculate the expectation value P1 and P2
Q: Two identical bosons of mass m are placed in a one-dimensional potential 1 v(x)=mo'x². The bosons…
A:
Q: Assume a flat Friedmann-Robertson-Walker universe, dominated by a fluid with equation of state P =…
A:
Q: PROBLEM 3. Calculate the following commutator: [L, f(r)], where L is the operator of orbital…
A: Note that the orbital angular momentum operator (L) may be expressed in spherical polar form from…
Q: Using the properties of Poisson's brackets, show the following relations: (1) [Ly, L] = Lx (ii) [y,…
A: we know that, Lx=ypz-zpyLy=zpx-xpzLz=xpy-ypx
Q: Estimate the non-relativistic degeneracy pressure at the center of a 1.4 Msun neutron star…
A: The mass of the neutron star is given as, M=1.4MSun The mass of sun is given as, MSun=1.989×1030 kg.…
Q: Show that exp(i*m*phi) is an eigenfunction of L(hat)z and find the corresponding eigenvalue
A:
Q: The energy eigenvalues of a particle in a 3-D box of dimensions (a, b, c) is given by ny E(nx, ny,…
A:
Q: by using the annihilation operator prove that the wave function of ground state for harmonic…
A: Concept used: Annihilation operator acts on state and lowers by 1. It acts on ground state to give…
Q: Hawkings realized that the perfectly thermal nature of black-hole radiation and also further in the…
A: Introduction: The observation made by physicist Stephen Hawking regarding black hole radiation and…
Q: The Hamiltonian of a system with two states is given by the following expression: ħwoox H where ôx =…
A:
Q: The eigenfunctions satisfy the condition | Vi (x)m(x)dx = &nm , &nm = 1 if n %3D %3D = m , otherwise…
A:
Q: Suppose there is a two state system with energies ε_0 = 0 and ε_1 = kT that follows the Boltzmann…
A:
Q: Using the equations of motion for operators in the Heisenberg representation, calculate the…
A: The Heisenberg's equation of motion is given by ihdAdt=A(t), H(t)+ih ∂A∂tThe schrodinger's…
Q: What is the minimum possible energy for fice (noninteracting) spin-3/2 particles of mass m in a…
A: Write an expression for energy for a one-dimensional box of length L
Q: Show that the expectation value for the speed of a particle, ( v ), is: = 8kBT πm using the…
A: We will first write expression for expectation value for speed of particle. Then we will we…
Step by step
Solved in 3 steps
- Consider a particle of mass m moving in one dimension with wavefunction $(x) 2 2πα sin for VI and zero otherwise. Is the wave function an eigenfunction of p? If so, what is the eigenvalue?A boat on the surface of the water suffers an explosion. Who hears the explosion first, a second boat 1 km away, or a whale swimming 4km deep directly under the boat? (βwater = 2.2 x 109 Pa, ρwater = 1000 kg/m3)Consider a Maxwellian distribution: f(v) = (a) Find (vx) (b) Find (v²) 1 v² v² (PAV) P ( 15 +52 +12²) exp √π)³ Vin (c) Find (mv²/2) (d) Find the flux l' crossing the YZ plane (Suppose the particle density is n)
- A proton is in an infinite square well potential given by Equation 6-21 with L = 1 fm.(a) Find the ground-state energy in MeV. (b) Make an energy-level diagram for this system. Calculate the wavelength of the photon emitted for the transitions (c) n = 2 to n = 1, (d) n = 3 to n = 2, and (e) n = 3 to n = 1.The coherent states for the one-dimensional harmonic oscillator are defined as eigenstates of the operatorof annihilation a (which is non-Hermitian):a |λ⟩ = λ |λ⟩ (1)where λ is a complex number in general. a)prove that is a normalized consistent state. b)Show that the above state satisfies the minimum uncertainty relation, i.e., show thatin quantum mechanics ; calculate the eigenvalue of these operators L2 , Lz when l equal to 6 ?
- ext cenb. Consider a system whose states are given in term of complete and orthonormal set of kets |1>, |2 >, [3 >,14 > as follows: 1 1p >= |1 > + 기2 > +2|3 > + 기4 > i 214> Where the kets |n > are eigenstates of an observable A defined on the system as follows: 2 A]n > = na|n > with n = 1,2,3,4 and with a a constant number. have 4) eiyen vealue 1. If A is measured, which values will be found and with which probabilities? 2. Find the expectation value of A for the state |Ø >. 3. Assume that the state 14> is found after the measurement of A. If A is measured again immediately, which states will be found and with which probabilities? 4. Find the expectation value of A if the system is in the state |4 >. 5. Assume B another observable defined on the system, which is compatible with A. Write the uncertainty inequality between A and B. 6. If B is measured, which states will be found and with which probabilities?Provide a sketch of the dependence of the ionization probability on the frequency of the perturbation, P(w). What is the ionization threshold otherwise known as the minimum frequency required to ionize the particle? (Please type answer note write by hend)Use Dirac notation to calculate the separations in energy levels for a spin system consisting of two protons.
- Consider a system spin-1/2 system, denoted by A, interacting with another system spin-1/2 system, denoted by B, such that the state of the combined system is AB) a++ B|-+). Find (a) the density matrix PA for system A corresponding to this state and (b) obtain the formulas for (()).(a) Construct the completely antisymmetric wave function ψ(xA, xB, xC) for three identical fermions, one in the state ψ5, one in the state ψ7, and one in the state ψ17. (b) Construct the completely symmetric wave function ψ(xA, xB, xC) for three identical bosons, (i) if all three are in state ψ11, (ii) if two are in state ψ1 and one is in state ψ19, and (iii) if one is in the state ψ5, one in the state ψ7, and one in the state ψ17.(*) Consider a large system of volume V containing N non-interacting particles. Take some fixed subvolume V « V. Calculate the probability to find N particles in volume V. Now assume that both N and V tend to oo, but in such a way that the particle number density is fixed: N/V →n = const. a) Show that in this limit, the probability py to find N particles in volume V (both N and V are fixed, N «N) tends to the Poisson distribution whose average is (N) = nV. Hint. This involves proving Poisson's limit theorem. b) Prove that ((N – (N))²)/2 (N) 1 V(N) (so fluctuations around the average are very small as (N) > 1). c) Show that, if (N) > 1, pN has its maximum at N = (N) = nV; then show that in the vicinity of this maximum, 1 e-(N-nV)²/2nV /2TNV Hint. Use Stirling's formula for N! (look it up if you don't know what that is). Taylor- expand In pN around N = nV.