HW6: Central Forces.
1: Orbital Angular Momentum
1. Let |n, l, mi denote the simultaneous eigenstates
q of L , Lz . Show that
|n, l, mi = alm Llm
|n, l, li. Here alm =
2. Show that in any represe
HW3: Simple Problems
1: Dirac Delta Function
1. Prove that (ax) = (x)/|a|.
2. Prove that (f (x) =
(x xk )/|f 0 (xk )|. Here f 0 (x) = df /dx and xk are zeros of the
function, namely f (xk ) = 0.
3. Evaluate (x2 a2
Problem Set 2
1. Two angular momenta j1 = and j2 = 1 are to be added to give a
total angular momentum j.
(a) What are the possible values of the total angular momentum j?
(b) How many states are there in the coupled rep
PRL 118, 060502 (2017)
PHYSICAL REVIEW LETTERS
10 FEBRUARY 2017
Resource Destroying Maps
Zi-Wen Liu,1,* Xueyuan Hu,2 and Seth Lloyd3
Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology,
arXiv:quant-ph/0101003v2 3 Nov 2001
An Analysis of Completely-Positive
Trace-Preserving Maps on M2
Mary Beth Ruskai
Department of Mathematics
University of Massachusetts Lowell
Lowell, MA 01854 USA
Department of Mathe
HW4: Problems in 1-Dimension
1: Simple Potentials
1. Solve time independent Schr
odingers equation(TISE) for a Dirac Delta potential at the origin.
2. Consider a periodic potential V (x) = V (x + a). Solve Schrodingers
HW2: More Matrices, Functions
1, the Pauli matrices are defined as
1 0 :=
x 1 :=
y 2 :=
z 3 :=
Answer the following questions. With i :=
1: More Matrices
PH- 422: Quantum Mechanics-II
Problem Set 1
1. Find the exception value of L2 and Lz in the state (r) = R(r)( 23 Y1,1 (, )
i 23 Y1,1 (, ).
2. A particle is in a l = 1 state and is known to have angular momentum
in the x direction equal to ~
Electrical Engineering: An Overview
The International System of Units
Circuit Analysis: An Overview
Voltage and Current
The Ideal Basic Circuit Element
Power and Energy
What is the lumped-pa
Aim To determine the wavelength of polychromatic light and the
angular dispersive power of a diffraction grating.
Spectrometer, prism, diffraction grating, polychromatic
An arrangement consisting
Analysis Of Experimental Data
1. Error Analysis And Accuracy Of Measurement
All physical measurements are subject to various types of errors. It is
important to plan any experiment with an accuracy appropriate to its
purpose and perform i
Resonance in Series RLC circuit
To examine the behavior of current, voltage, and impedance of a series
resonant circuit with respect to frequency. To determine Q-factor and
bandwidth for various values of the damping resistor.
Determination of (e/m) ratio of an electron
Aim: To determine the specific charge of an electron ( / ) using an
electron beam in crossed electric and magnetic fields of variable
Narrow Beam Tube
Variable DC Volta
To measure the magnetic field produced by the Helmholtz coil.
To determine the torque experienced by a current carrying loop,
suspended between the Helmholtz coils, as a function of:
(i) the strength of the magnetic moment
This experiment requires you to determine the centrifugal force experienced by a
car which is at rest on a track rotating with a constant angular velocity (See
Fig.1). The car comes to rest (after an initial transient motion)
Thermal Conductivity By Lees Disc
Measurement of thermal conductivity of a poor/bad conductor by electrically
heated Lees disc apparatus
The electrically heated Lees disc apparatus for the
measurement of thermal conductivity of
Objective: To obtain the wavelength of Sodium light using Fresnels bi-prism.
Apparatus: Optical rail with uprights, sodium lamp, bi-prism, convex lens, slit
and micrometer eyepiece.
Fig. 1: Formation of two coherent virtua