Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [209]
11 Bloch (1976), p. 23.
12 Bloch (1976), p. 23.
13 Abragam (1988), p. 31.
14 Bloch (1976), pp. 23–4.
15 The equation was rediscovered in 1927 by Oskar Klein and Walter Gordon and became known as the Klein-Gordon equation. It applies only to spin zero particles.
16 Moore (1989), quoted p. 196.
17 Moore (1989), quoted p. 191.
18 The title of Schrödinger's paper signalled that in his theory the quantisation of an atom's energy levels was based on the allowed values, or eigenvalues, of electron wavelengths. In German, eigen means 'proper' or 'characteristic'. The German word eigenwert was only half-heartedly translated into English as eigenvalue.
19 Cassidy (1992), quoted p. 214.
20 Moore (1989), quoted p. 209. Letter from Planck to Schrödinger, 2 April 1926.
21 Moore (1989), quoted p. 209. Letter from Einstein to Schrödinger, 16 April 1926.
22 Przibram (1967), p. 6.
23 Moore (1989), quoted p. 209. Letter from Einstein to Schrödinger, 26 April 1926.
24 Cassidy (1992), quoted p. 213.
25 Pais (2000), quoted p. 306.
26 Moore (1989), quoted p. 210.
27 Mehra and Rechenberg (1987), Vol. 5, Pt. 1, quoted p. 1. Letter from Pauli to Pascual Jordan, 12 April 1926.
28 Cassidy (1992), quoted p. 213.
29 Cassidy (1992), quoted p. 213. Letter from Heisenberg to Pascual Jordan, 19 July 1926.
30 Cassidy (1992), quoted p. 213.
31 Cassidy (1992), quoted p. 213. Letter from Born to Schrödinger, 16 May 1927.
32 Mehra and Rechenberg (1987), Vol. 5, Pt. 2, quoted p. 639. Letter from Schrödinger to Wilhelm Wien, 22 February 1926.
33 Mehra and Rechenberg (1987), Vol. 5, Pt. 2, quoted p. 639. Letter from Schrödinger to Wilhelm Wien, 22 February 1926.
34 Pauli, Dirac and the American Carl Eckhart all independently showed that Schrödinger was correct.
35 Mehra and Rechenberg (1987), Vol. 5 Pt. 2, quoted p. 639. Letter from Schrödinger to Wilhelm Wien, 22 February 1926.
36 Moore (1989), quoted p. 211.
37 Moore (1989), quoted p. 211.
38 Cassidy (1992), quoted p. 215. Letter from Heisenberg to Pauli, 8 June 1926.
39 Cassidy (1992), quoted p. 213. Letter from Heisenberg to Pascual Jordan, 8 April 1926.
40 Heisenberg's paper was received by the Zeitschrift für Physik on 24 July and was published on 26 October 1926.
41 Pais (2000), quoted p. 41. Letter from Born to Einstein, 30 November 1926. Not included in Born (2005).
42 Bloch (1976), p. 320. In the original German: Gar Manches rechnet Erwin schon Mit seiner Wellenfunktion. Nur wissen möcht' man gerne wohl Was man sich dabei vorstell'n soll.
43 Strictly speaking it should be the square of the 'modulus' of the wave function. Modulus is the technical term for taking the absolute value of a number regardless of whether it is positive or negative. For example, if x=-3, then the modulus of x is 3. Written as: |x| = |-3|=3. For a complex number z=x+iy, the modulus of z is given by |z| = x2+y2.
44 The square of a complex number is calculated as follows: z=4+3i, z2 is in fact not z×z, but z×z* where z* is called the complex conjugate. If z=4+3i, then z*=4-3i.
Hence, z2=z×z*=(4+3i)×(4-3i)=16-12i+12i-9i2=16-9(-1)2=16–9(-1)=16+9=25.
If z=4+3i, then the modulus of z is 5.
45 Born (1978), p. 229.
46 Born (1978), p. 229.
47 Born (1978), p. 230.
48 Born (1978), p. 231.
49 Born (2005), p. 81. Letter from Born to Einstein, 15 July 1925.
50 Born (2005), p. 81. Letter from Born to Einstein, 15 July 1925.
51 Pais (2000), quoted p. 41.
52 Pais (1986), quoted p. 256.
53 Pais (2000), quoted p. 42.
54 The second paper was published in the Zeitschrift für Physik on 14 September.
55 Pais (1986), quoted p. 257.
56 Pais (1986), quoted p. 257.
57 Once again, technically speaking it is the absolute or modulus square of the wave function. Also, technically, rather than the 'probability', the absolute square of the wave function