Attempt frequency in tunneling

American Journal of Physics

Volumn 66, Issue 12, 1998, Pages 1119-1122

  Price, Peter J ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032352453     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19053     Document Type: Article

References (12)

1. J. R. Oppenheimer, "Three notes on the quantum theory of aperiodic effects," Phys. Rev. 13, 66-80 (1928). (See note no. 3.)
2. G. Gamow, "Zur Quantentheorie des Atomkerns," Z. Phys. 51, 204-212 (1928).
3. R. W. Gurney and E. U. Condon, "Quantum mechanics and radioactive disintegration," Phys. Rev. 33, 127-140 (1929).
4. Complementary, mildly partisan, accounts of this development will be found in: E. U. Condon, "Tunneling - how it all started," Am. J. Phys. 46, 319-323 (1978), and V. Ya Frenkel, "George Gamow: World line 1904-1933," Sov. Phys. Usp. 37, 767-789 (1994).
5. Complementary, mildly partisan, accounts of this development will be found in: E. U. Condon, "Tunneling - how it all started," Am. J. Phys. 46, 319-323 (1978), and V. Ya Frenkel, "George Gamow: World line 1904-1933," Sov. Phys. Usp. 37, 767-789 (1994).
6. M. von Laue, "Notiz zur Quantentheorie des Atomkerns," Z. Phys. 52, 726-734 (1929).
7. For an English language version, see Sec. 50 in: L. D. Landau and E. M. Lifshitz, Quantum Mechanics - Non-relativistic Theory (Peragamon, New York, 1958).
8. For a truly free particle, this would apply to a wave packet. The more general application, such as to temporary trapping of a scattered particle, is in L. Eisenbud (dissertation, Princeton, 1948) and E. P. Wigner, "Lower limit for the energy derivative of the scattering phase shift," Phys Rev. 98, 145-147 (1955). The latter discusses scattering in terms of the equivalent spatial displacement dθ/dk. In the neighborhood of a resonance, it is not appropriate to consider a wave packet - which becomes distorted in transit as well as delayed - but the quantity defined by Eq. (13) retains its formal role, such as here.
9. P. J. Price, "Space charge in nanostructure resonances," Superlatt, Microstruct. 20, 253-260 (1996).
10. 2 values the doublet levels, due to the interaction of the two wells, merge in the local density of states but not in all properties.
11. M. G. Fuda, in "Time-dependent theory of alpha decay," Am. J. Phys. 52, 838-842 (1984), imposes on the Schrödinger equation an initial condition Ψ(x,0)=0 at and outside the outer boundary of the enclosing structure, and obtains an (approximate) solution for the probability of the particle remaining inside this boundary, for t;>0, that has an exponential decrease with time which is to be identified with the Gamow exponential decrease.
12. L. Mirsky, An Introduction to Linear Algebra (Oxford U.P., New York, 1961).