Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Spring 2015
End of term Exam (a)
1. What is an arbitrage opportunity? (1point)
a) An opportunity to make a profit without taking any risk
b) An investment opportunity that requires zero investment today with no losses in the future under any contingency, with
profit
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Fall 2015
Macroeconomics Practice Test 1
Fall 2015
1. The law of demand states that
A) consumers have unlimited demands for a good.
B) a higher price will lead to increased sales.
C) the price can never be too high for some consumers.
D) quantity demanded will vary
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Multiple Choice Questions in Basic Quantum Mechanics
1
Module 10: Time Independent Perturbation Theory
10.1 Consider a 4fold degenerate state with orthonormal eigenfunctions u1 , u2 , u3 and u4 . There is
g ; g 0 and all the other matrix elements are
a p
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 7: BraKet Algebra and Linear Harmonic Oscillator II
7.1
n are the normalized eigenkets of the Hamiltonian corresponding to the linear harmonic
oscillator problem. Thus H n
En n
n
1
2
n ; n
0,1, 2. The matrix element
n 1 x n is equal to
(a)
(b)
12
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 10: FAQs along with their solutions
1
Question 1: Consider a 2fold degenerate state with (normalized) eigen functions u1 and
u2 .Consider a perturbation H with
H11 =< 1H 1 >= 0, H22 =< 2H 2 >= 0 and
H12 = H21 =
Obtain the splitting and corres
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 6: Hydrogen Atom and Other Two Body Problem
6.1 For a spherically symmetric potential, the radial part of the Schrodinger equation is given
by:
d 2 R 2 dR r
dr 2 r dr
(c)
F r
R r
0 . The function F r is given by
l l 1 2
2 r2
(a)
(b)
2
E V r
2
l l 1
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 8: Angular Momentum  II
8.1
L Lx iLy e i
i cot ; Y1,1 C LY1,0 . The constant C is given
by
(a) C
1
2
1
(b) C
2
1
(c) C
6
1
(d) C
6
[Answer (a)]
8.2
L Lx iLy e i
i cot ; Y3,2 C LY3,1 . The constant C is given
by
1
10
1
(b
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
FAQs & their solutions for Module 2:
Simple Solutions of the onedimensional Schrodinger Equation
Question1: Determine the energy levels and the corresponding Eigen functions of
a particle of mass in a one dimensional infinitely deep potential well
charac
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
FAQs & their solutions for Module 1:
Introduction & Basic Mathematical Preliminaries
Question1: An electron of energy 200 eV is passed through a circular hole of radius
10  4 cm. What is the uncertainty introduced in the angle of emergence?
Solution1:
p
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
FAQs & their solutions for Module 3:
Linear Harmonic Oscillator
Question1:
function
At t 0 , a
linear harmonic oscillator is described by the wave
1
( x,0)
3
0 ( x)
i
2
3
(1)
2 ( x)
where n ( x) are the normalized eigenfunctions of the Schrodinger equatio
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Spring 2015
KZT bln
Net income
Net interest income (1)
Net fee and commissions
income
RoAE (2), p.a.
RoAA (2), p.a.
Cost of risk (2), p.a.
NIM (2), p.a.
Gross loans
Net loans
NPLs 90 days
Liquid assets
Total assets
9M 2013
173970
33921
22938
1.19%
0.89%
31Dec13
190
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 2: Simple Solutions of the onedimensional Schrodinger Equation
2.1 For a free particle, the most general solution of the 1dimensional Schrodinger equation is
given by
x.0
1
1
2
0
4
1
2
0
2
4
p
exp
1
2
0
2
2 p
exp
(b) a p
(d) a p
exp
1
4
p
exp
1
2
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
FAQs & their solutions for Module 8:
Angular MomentumII
Question1: The spin angular momentum operator for electron is given by
sx
1
1
1
x , s y y , s z z
2
2
2
(1)
Where x , y and z are Pauli spin matrices and are given by
0 1
0 i
1 0
,z
0 1
0
x ,
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 5: Angular Momentum  I
5.1
Y2,0
N P2
where P2
1
3
2
2
1 and
cos
constant N will be given by
(a)
(b)
(c)
(d)
5
2
5
2
5
4
5
4
[Answer (c)]
5.2
Y2,
(a)
(b)
(c)
(d)
k 2
k 2i
k
2
k
2i
2
[Answer (d)]
15
sin 2
16
1 k
e
2
. The value of k will be
. The no
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Problems
Module Name: Microscopic Theory of Superconductivity
Module No: VI
1. Work out the Cooper pair instability for the triplet pairing of two electrons.
2. In the Cooper pair problem there is always a bound state for nite kF .
Show that in three dime
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 9: The JWKB Approximation & Applications
Fig. 9.1
9.1
Consider a typical k 2 x
variation as shown in Fig. 9.1. We consider an exponentially
decaying solution in the region x
b:
x
x
1
exp
x
The solution in the region a
(a)
x
2
b
sin
k x
(b)
x
2
k x
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
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Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
FAQs & their solutions for Module 4:
Particle in a threedimensional box
Question1: For a free particle inside a cube, the potential energy variation of the form
V ( x, y , z )
for 0
x
L ; 0 y L; 0
everywhere else
z
L
(1)
Solve the Schrdinger equation and
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
FAQs & their solutions for Module 5:
Angular MomentumI
Question1: The operator representation of Lz is given by:
Lz i
(1)
(a) Solve the eigen value equation for Lz ; determine the eigen values and normalized eigen
functions.
(b)
Write the orthonormailty
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Multiple Choice Questions in Basic Quantum Mechanics
Module 1: Introduction & Basic Mathematical Preliminaries
2
1.1
(a)
2
(b)
2
(c)
(d)
2
2
1
r
1
r
1
r
1
r
1
r
0
4
r
4
r
r
[Answer (b)]
1.2
(a)
(b)
(c)
(d)
Consider a function given by
d2 f
dx 2
d2 f
dx 2
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
FAQs & their solutions for Module 7:
BraKet Algebra and LHOII
Question1: If A = P , show that P = A where is the adjoint of the operator .
Solution1:
A B = B A = B P
= PB
Since the above equation is valid for arbitrary B we have
P = A = conjugate of A
(
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 9
1
Problems
The JWKB Approximation
1
2 2
2 x .
Question 1: Assume V (x) =
Calculate the values of the turning points and show that the
energy eigenvalues as obtained by using the JWKB quantization condition is given by E = En =
(n + 1 ) , n = 0, 1
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
FAQs&theirsolutionsforModule6:
Hydrogenlikeatomsandothercentralpotentials
Question1:Inspectroscopytheenergylevelsareusuallywritteninwavenumberunitswhich
areobtainedbydividing En byhc:
Tn =
En
Z2
=
R
hc
n2
(1)
Usingtheexpressionfor En ,showthattheRydbergco
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 4: Simple Applications of Schrodinger Equation
4.1
For a potential energy variation of the form
V x, y,z
0 for 0 x L, 0 y L, 0 z L
everywhere else
2
2
the energy eigenvalues are given by E K nx n y nz2 ; nx ,n y ,nz 1, 2,3,. .
2
2 L2
2 2
(b) K
8 L2
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Winter 2014
Module 3: Linear Harmonic OscillatorI
3.1
Let
n
x represents the normalized eigenfunctions corresponding to the linear harmonic
oscillator problem n 0,1, 2,3. .
0
x
N exp
1
2
2
;
x and
. Determine
the normalization constant N .
(a) N
(b) N
(c) N
2
2
(d)
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Spring 2015
The CAL provided by one month Tbills and a broad index of
common stocks the CML; the SML graphs individual asset risk
premium as a function of asset risk. At the point where =1 on the
horizontal axis, we can read off vertical axis the E(r) on the M
portf
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Spring 2015
KazakhBritish Technical University
Business School
Department of Management
ESSAY
Increase your influence at work
Done by:
Roza Redyassebova
Almaty 2014
This Book is about how to impact to the people especially with whom you work
and how develop your ski
Kazakhstan Institute of Management, Economics and Strategic Research
introduction
ECONOMICS 101

Fall 2014
1. In the macro economy, total income never equals total expenditures in practice.
You chose:
Unanswered
Correct
False
answer:
Actually, total income and total expenditures are two sides of the same coin, so
Explanation:
they're always equal.
2. GNP is de