1. Quantum mechanics and the Copenhagen Interpretation
                               
                               
Contents:
Copenhagen Interpretation of Young’s Double slit
The Quantum atom
Heisenberg uncertainty principle
The Einstein Bohr debate
Quantum Mechanics

2. Copenhagen Interpretation – Demo laser
Electrons interfere even when sent one at a time (why?)
Copenhagen:  = Schrödinger wave function of electron
“Probability waves” interfere (2 = probability)
TOC

3. Heisenberg Uncertainty Principle
Let’s find an electron
Photon changes the momentum of electron
x  
p  h/ (smaller , bigger p)
xp > h/4
x – uncertainty of position
p - uncertainty of momentum
Et > h/4
E - uncertainty of energy (Range)
t - uncertainty of time (Range)
if x = 3.5 ± 0.2 m, x = 0.4 m – if you are using h/4π
Chris,
The uncertainty in a coordinate or momentum is its variance (root mean square error). So use the total range .2 .
-Jack
*******************************************************
Jack S. Semura
Physics Department, Portland State University Portland, OR 97207
Quoting "Murray, Christopher"
> One more quick question - when you do calculations with the Heisenberg
> uncertainty principle, what do you use as the uncertainty?
> 
> Eg x = 3.3 +/- .1 m, is the uncertainty of x .1, or is it the range .2?
> Chris
> -----Original Message-----
> From: Jack Semura
> Sent: Wednesday, February 17, :34 PM
> To: Murray, Christopher
> Cc:
> Subject: Re: Uncertain about Heisenberg
> Hi Chris,
> Great to hear from you! I often wonder what you're doing you when I
> hear about news from Tualatin.
> About the uncertainty principle:
> Wikipedia is correct. The Heisenberg uncertainty product cannot be
> less than (1/2)h-bar. (As a general rule of thumb, I tend to trust
> Wikipedia more than just about any General Physics text.)
> A couple additional points about the uncertainty principle:
> (1) The uncertainty product is between specific *conjugate*
> variable pairs x and p (the position and its conjugate momentum).
> (2) I tend to agree with the viewpoint that the uncertainty
> principle is a fundamental property of nature. It's not a result of
> us making an observation. So I don't really like the "Heisenberg
> light microscope" explanation that a lot of popular books use.
> Hope this helps.
> Regards,
> -Jack
> Quoting "Murray, Christopher"
>> Erik and Jack -
>> 
>> I have a question about the Heisenberg uncertainty principle -
>> Wikipedia, The IB data packet, and two other physics texts in my room
>> state that the product of the uncertainty of position-momentum or
>> energy-time cannot be smaller than h/(4pi) or h-bar/(2pi)
>> Giancoli (the text we use), and my old college modern physics text
>> state that they cannot be bigger than
>> h/(2pi) or h-bar
>> perhaps the difference is that when giancoli solves problems in his
>> text he uses the range of a value, not what we would normally call
>> the uncertainty.
>> For example, in a problem with x = 4.5 +/- 0.1 m, he plugs in the
>> uncertainty of x to be 0.2 m, and one of the other texts that I
>> looked at uses the uncertainty in this situation to be 0.1 m
>> Do you suppose that is the difference?
>> Chris
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4. Heisenberg Uncertainty Principle
xp > h/4
Et > h/4
Strange quantum effects:
Observation affects reality
Energy is not conserved (for t)
Non determinism
Quantum randomness
Quantum electrodynamics
Example: What is the uncertainty in the position of a kg baseball with a velocity of 37.0 ± 0.3 m/s?
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5. Example: What is the uncertainty in the position of a 0
Example: What is the uncertainty in the position of a kg baseball with a velocity of 37.0 ± 0.3 m/s.
The uncertainty of momentum is (0.145 kg)(0.6 m/s) = kg m/s
And now we use xp > h/4:
x( kg m/s) > (6.626E-34 Js)/(4), x > 6.1E-34 m
so x is > 6.1E-34 m
So not really very much.

6. HL Paper 2
B4 3 d, p. 36
2012
????????
They use ½ Range…

7. xp > h/4 Et > h/4
Example: The electron stays in the first excited state of hydrogen for a time of approximately Δt = 1.0 x s
Determine the uncertainty in the energy of the electron in the first excited state.

8. HL Paper 2
B3 1 e, p. 34
2011

9. Heisenberg Uncertainty
Whiteboards:
Heisenberg Uncertainty
1 | 2
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10. For what period of time is the uncertainty of the energy of an electron ΔE = 2.5 x 10-19 J?
Et > h/4
(2.5 x J)t > h/4
t = 2.1 x s W
t = 2.1 x s

11. You know an electron’s position is ±
You know an electron’s position is ±.78 nm, what is the minimum uncertainty of its velocity? (4)
xp > h/4
p = mv
m = 9.11 x kg
x = 2x0.78 x 10-9 m = 1.56E-9 m
(1.56 x 10-9 m)p > (6.626 x Js)/4
p =3.38 x kg m/s
(3.38 x kg m/s) = (9.11 x kg)v
v = ≈ 3.7 x 104 m/s
Chris,
The uncertainty in a coordinate or momentum is its variance (root mean square error). So use the total range .2 .
-Jack
Physics Department, Portland State University Portland, OR 97207
Jack S. Semura
*******************************************************
Quoting "Murray, Christopher"
> uncertainty principle, what do you use as the uncertainty?
> One more quick question - when you do calculations with the Heisenberg
> Eg x = 3.3 +/- .1 m, is the uncertainty of x .1, or is it the range .2?
> 
> Chris
> -----Original Message-----
> To: Murray, Christopher
> Sent: Wednesday, February 17, :34 PM
> From: Jack Semura
> Subject: Re: Uncertain about Heisenberg
> Cc:
> Hi Chris,
> hear about news from Tualatin.
> Great to hear from you! I often wonder what you're doing you when I
> About the uncertainty principle:
> Wikipedia more than just about any General Physics text.)
> less than (1/2)h-bar. (As a general rule of thumb, I tend to trust
> Wikipedia is correct. The Heisenberg uncertainty product cannot be
> A couple additional points about the uncertainty principle:
> (1) The uncertainty product is between specific *conjugate*
> variable pairs x and p (the position and its conjugate momentum).
> principle is a fundamental property of nature. It's not a result of
> (2) I tend to agree with the viewpoint that the uncertainty
> light microscope" explanation that a lot of popular books use.
> us making an observation. So I don't really like the "Heisenberg
> Hope this helps.
> Regards,
> -Jack
> Quoting "Murray, Christopher"
>> 
>> Erik and Jack -
>> I have a question about the Heisenberg uncertainty principle -
>> state that the product of the uncertainty of position-momentum or
>> Wikipedia, The IB data packet, and two other physics texts in my room
>> energy-time cannot be smaller than h/(4pi) or h-bar/(2pi)
>> h/(2pi) or h-bar
>> state that they cannot be bigger than
>> Giancoli (the text we use), and my old college modern physics text
>> the uncertainty.
>> text he uses the range of a value, not what we would normally call
>> perhaps the difference is that when giancoli solves problems in his
>> looked at uses the uncertainty in this situation to be 0.1 m
>> uncertainty of x to be 0.2 m, and one of the other texts that I
>> For example, in a problem with x = 4.5 +/- 0.1 m, he plugs in the
>> Do you suppose that is the difference?
>> Chris W
v = 3.7 x 104 m/s

12. The Einstein-Bohr debate
Einstein objected to quantum randomness
“God does not play dice”
Attacked either Heisenberg uncertainty, or complementarity
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13. The Einstein-Bohr debate
Einstein would challenge Bohr at conferences
Front: Bohr, Heisenberg, Pauli, Stern, Meitner, Ladenburg
TOC
For example…

14. Gedanken experiment (to disprove complementarity)
Detect which slit the electron went through with light beam (particle behaviour)
If interference pattern appears, then we have both wave and particle behaviour
Complementarity says it must be either s d
Electron beam
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15. Bohr would take a walk
E. Fermi, N. Bohr

16. Bohr’s reply No interference pattern would happen
The light that detected the electron would change its momentum
To have interference, electrons must be monochromatic
 = h/p
Complementarity is intact s d
Electron beam
TOC

17. Quantum mechanics Bohr always prevailed
(God apparently does play dice)
Three “types” of physics
Newtonian/classical - big stuff
Relativity - speeds close to c
Quantum mechanics - physics of the atom
Correspondence principle
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