Schr¨odinger Equation
an introduction
Febdian Rusydi
PHOTON – University of Airlangga
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
1 Mechanism of Motion review so far dynamics
2 Dotting Yourℑ’s and Crossing Your h’s!
wave equation for electron operators
QUIZ #1 DIMULAI DALAM 5 MENIT KE DEPAN
Buat jarak antaranda
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Tidak diperkenankan meminjam alat tulis dan kalkulator. Waktu 20 menit tanpa perpanjangan.
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
Quiz (20 minutes)
At timet = 0 a particle is represented by the wave function
Ψ(0,x) = (
A(a2−x2) if −a≤x ≤+a,
0 otherwise.
1 Determine the normalization constantA.
2 Sketch Ψ(0,x) as a function ofx.
3 What is the expectation value of x (at timet= 0).
4 Find is the expectation value of p (at timet = 0). Note: You cannot get it frommdhxi/dt, why?
foundation principle
1 The very basic principle
probability
the very basic principle
⇓
|Ψ(t,x)|2 = PDF Born’s statistical
interpretation
2 The basic assumptions
de Broglie hypothesis
the first assumption
⇓
wave-particle duality
they behave symmetrically
⇓
particle has wavelength
λ=~/p
Heisenberg’s Uncertainty Principle
the second assumption
⇓
σxσp >~
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
review so far
dynamics
consequence of de Broglie hypothesis
Definition (mechanism)
consequence of de Broglie hypothesis
Definition (mechanism)
Mechanism is the way that something works like the way it does. Mathematically mechanism is stated as EOM. Since EOM is for dynamic object, a working only happen if the object is dynamics.
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
review so far
dynamics
consequence of de Broglie hypothesis
Definition (mechanism)
Mechanism is the way that something works like the way it does. Mathematically mechanism is stated as EOM. Since EOM is for dynamic object, a working only happen if the object is dynamics.
Dynamic objects: particle and wave.
consequence of de Broglie hypothesis
Definition (mechanism)
Mechanism is the way that something works like the way it does. Mathematically mechanism is stated as EOM. Since EOM is for dynamic object, a working only happen if the object is dynamics.
Dynamic objects: particle and wave.
EOM particle is Newton 2nd law → theory of particle for particle.
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
review so far
dynamics
consequence of de Broglie hypothesis
Definition (mechanism)
Mechanism is the way that something works like the way it does. Mathematically mechanism is stated as EOM. Since EOM is for dynamic object, a working only happen if the object is dynamics.
Dynamic objects: particle and wave.
EOM particle is Newton 2nd law → theory of particle for particle.
consequence of de Broglie hypothesis
Definition (mechanism)
Mechanism is the way that something works like the way it does. Mathematically mechanism is stated as EOM. Since EOM is for dynamic object, a working only happen if the object is dynamics.
Dynamic objects: particle and wave.
EOM particle is Newton 2nd law → theory of particle for particle.
EOM wave is Wave Equation → theory of wave for wave. Theory of particle for light → photon.
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
review so far
dynamics
dotting your
ℑ
’s and crossing your
h
’s!
Laplacian operator (cartesian):
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
wave equation for electron
operators next
commentary on the Schr¨odinger equation
commentary on the Schr¨odinger equation
− ~
2
2m ∇
2+V
Ψ =ℑ~ ∂
∂t Ψ
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
wave equation for electron
operators next
commentary on the Schr¨odinger equation
It is a different form of the conservation energy principle. It was published by Ewrin Schr¨odinger in 1925; he later won the Noble Prize at 1933 for that.
A year before, in 1924, Werner Heisenberg published a seemingly different theory to explain quantum physics. Schr¨odinger succeed to show that both equations are equally the same. Their both equations found the ”quantum
commentary on the Schr¨odinger equation
− ~
2
2m ∇
2+V
Ψ =ℑ~ ∂
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
wave equation for electron
operators next
commentary on the Schr¨odinger equation
commentary on the Schr¨odinger equation
sense that (1) it is EOM for non-relativistic case and (2) it relates the time and space derivatives of the wave functions. The kinetic energy form,T =− ~
2
2m ∂2Ψ
∂x2
Outline Mechanism of Motion Dotting Yourℑ’s and Crossing Yourh’s!
wave equation for electron
operators
next
position, momentum, kinetic
To find the value→calculate the expectation value of the operator.
Z +∞
