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

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

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" <cmurray@ttsd.k12.or.us>: > 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 [mailto:semuraj@pdx.edu] > Sent: Wednesday, February 17, 2010 3:34 PM > To: Murray, Christopher > Cc: 'bodegom@pdx.edu' > 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" <cmurray@ttsd.k12.or.us>: >> 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 TOC

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 0.145 kg baseball with a velocity of 37.0 ± 0.3 m/s? TOC

Example: What is the uncertainty in the position of a 0 Example: What is the uncertainty in the position of a 0.145 kg baseball with a velocity of 37.0 ± 0.3 m/s. The uncertainty of momentum is (0.145 kg)(0.6 m/s) = 0.0870 kg m/s And now we use xp > h/4: x(0.0870 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.

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

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 10-10 s Determine the uncertainty in the energy of the electron in the first excited state.

HL Paper 2 B3 1 e, p. 34 2011

Heisenberg Uncertainty Whiteboards: Heisenberg Uncertainty 1 | 2 TOC

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 10-19 J)t > h/4 t = 2.1 x 10-16 s W t = 2.1 x 10-16 s

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 10-31 kg x = 2x0.78 x 10-9 m = 1.56E-9 m (1.56 x 10-9 m)p > (6.626 x 10-34 Js)/4 p =3.38 x 10-26 kg m/s (3.38 x 10-26 kg m/s) = (9.11 x 10-31 kg)v v = 37102 ≈ 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" <cmurray@ttsd.k12.or.us>: > 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, 2010 3:34 PM > From: Jack Semura [mailto:semuraj@pdx.edu] > Subject: Re: Uncertain about Heisenberg > Cc: 'bodegom@pdx.edu' > 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" <cmurray@ttsd.k12.or.us>: >>  >> 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

The Einstein-Bohr debate Einstein objected to quantum randomness “God does not play dice” Attacked either Heisenberg uncertainty, or complementarity TOC

The Einstein-Bohr debate Einstein would challenge Bohr at conferences Front: Bohr, Heisenberg, Pauli, Stern, Meitner, Ladenburg TOC For example…

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 TOC

Bohr would take a walk E. Fermi, N. Bohr

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

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 TOC