We have intuition about temperature: cold vs hot etc.
But what is temperature? What does it measure?
Solid objects tend to expand at higher temperature.
Volume of a gas also increases with temperature.
When two objects
[SSM] For the hydrogen atom, as n increases, does the spacing of
adjacent energy levels on an energy-level diagram increase or decrease?
Determine the Concept Examination of Figure 35-4 indicates that as n increases,
Applications of the Schrdinger Equation
Sketch (a) the wave function and (b) the probability density function
for the n = 5 state of the finite square-well potential.
Determine the Concept Looking at the graphs in the text
[SSM] The approximate total energy of a particle of mass m moving
at speed u < c is (a) mc2 + 12 mu 2 , (b) 12 mu 2 , (c) cmu, (d) mc2, (e) 12 cmu .
Determine the Concept The total relativistic energy E of a par
p = mu
But this quantity is no longer conserved, due to the
transformation of velocities between frames.
Consider an observer A at rest in frame S and observer
B at rest in frame S, moving wrt S at v (+x direction).
Infinite Square Well in 3D
Schrodinger Equation in 3D
Often work in spherical coordinates.
f dr f d f d f
x dx r dx dx
r = x2 + y2 + z 2
x2 + y2 + z 2
(l m )!
(l + m )!
De Broglie Hypothesis
We have seen that radiation has dual behavior:
Wave-like and particle-like.
In 1924 de Broglie suggested that the same is true
Specifically, he proposed that frequency and
wavelength can be associated with an electron
Matter is not continuous it is quantized.
Idea dates back to Democritus (Greece, 450 BC).
First scientific arguments appear in 18th 19th century
Eg, Avogadros claim that 22.4 liter volume of a gas
contains the same number of molecules at
Heat is the transfer of energy between two objects due to
their difference in temperature.
Already saw that temperature (and the internal energy of
an object/system) is related to the kinetic energy of
When two objects are in thermal co
Light is an electromagnetic wave.
Visible light is an electromagnetic wave at very high frequency,
short wavelength (<10-6 m).
Intuition: light travels in a straight line.
Maxwells equations can be reduced to the wave equation.
Solutions are el
Reference frame: a coordinate system.
Could be attached to a particular spot in the system.
Could be moving.
Inertial reference frame: reference frame in which Newtons
Basically, a reference frame that is not accelerat
Interference and Diffraction
We described light in terms of geometrical optics.
Treat light as rays, emphasizes the particle nature of
Essentially ignores the wave-like nature of light.
In some situations, the wave-like nature becomes
Second Law of Thermodynamics
Consider a mass m, at height h above the surface of the
Has gravitational potential energy mgh.
Can use this potential energy to do work.
Let the mass drop and inelastically collide with the Earths
We know we need waves to describe an electron, but what
equation should it come from?
+ V ( x, t ) ( x, t ) = i
( x, t )( x, t )dx = 1
Normalized so that:
We have described the basic properties of reflection and
Reflection angle = incidence angle
Refraction: Snells law n1 sin1 = n2 sin2.
Now use these laws to understand how optical images are
created with mirrors and lenses.