Calculate the probability current corresponding to the wave function ei ikr where ² = x² + y² + 2² [ Y = r
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- The longest wavelength in the Pfund series is 7459 nm. Find the series limit.In scanning tunnelling microscope the tunnelling current is proportional to the transmission probability T. Suppose the gap potential energy V is greater than the electron energy E by V-E-=4.0 eV. Calculate the ratio of current when the needle is moved from L1=0.20nm to L2=0.35nm from the surface? Please enter your answer with 2 decimals.(a) Show that the terms in Schrödinger’s equation have the same dimensions. (b) What is the common SI unit for each of these terms?
- Show that the uncertainty principle can be expressed in the form ∆L ∆θ ≥ h/2, where θ is the angle and L the angular momentum. For what uncertainty in L will the angular position of a particle be completely undetermined?Consider the electron-hole overlap integral Mnn for a quantum well given by: Mn Pen (2) Pnn (z) dz. %3D - 00 n' and zerd (i) Show that Mon is unity if n otherwise in a quantum well with infinite barriers. (ii) Show that Mon is zero if (n-n') is an odd number in a quantum well with finite barriers.Show that the following function Y(0,9)= sin 0 cos e eiº is the solution of Schrödinger 1 1 equation: sin 0 21 sin 0 00 Y(0,0)= EY (0,9) and find the sin 0 dp? energy, E.
- Verify the law of addition of quantum mechanical amplitude in case of neutron diffraction in single crystal.A quantum system is described by a wave function (r) being a superposition of two states with different energies E1 and E2: (x) = c191(r)e iEit/h+ c292(x)e¯iE2t/h. where ci = 2icz and the real functions p1(x) and p2(r) have the following properties: vile)dz = ile)dz = 1, "0 = rp(x)T#(x)l& p1(x)92(x)dx% D0. Calculate: 1. Probabilities of measurement of energies E1 and E2 2. Expectation valuc of cnergy (E)An electron is in an infinite potential well of width 364 pm, and is in the normalised superposition state Ψ=cos(θ) ψ5-sin(θ) i ψ8. If the value of θ is -1.03 radians, what is the expectation value of energy, in eV, of the electron?