New PDF release: Mathematics, Science and Epistemology, Philosophical Papers

By Imre Lakatos

ISBN-10: 0521280303

ISBN-13: 9780521280303

Imre Lakatos' philosophical and medical papers are released right here in volumes. quantity I brings jointly his very influential yet scattered papers at the philosophy of the actual sciences, and contains one vital unpublished essay at the impact of Newton's medical success. quantity 2 provides his paintings at the philosophy of arithmetic (much of it unpublished), including a few severe essays on modern philosophers of technological know-how and a few recognized polemical writings on political and academic concerns.

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Extra resources for Mathematics, Science and Epistemology, Philosophical Papers

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28). For the quantum mechanical results that we require we shall be concerned only with stationary states, known sometimes as eigenstates. The wave functions for these states may be referred to as eigenfunctions and the associated energies E as the eigenvalues. The details of the methods of solving the Schro¨dinger equation for c and E for various systems do not concern us here but may be found in books listed in the bibliography. We require only the results, some of which will now be discussed.

1 illustrates one photon of such radiation travelling along the x axis. The electric component of the radiation is in the form of an oscillating electric field of strength E and the magnetic component is in the form of an oscillating magnetic field of strength H. These oscillating fields are at right angles to each other, as shown, and, if the directions of the vectors E and H are y and z respectively, then Ey ¼ A sinð2pnt À kxÞ Hz ¼ A sinð2pnt À kxÞ ) ð2:1Þ where A is the amplitude. Therefore, the fields oscillate sinusoidally with a frequency of 2pn and, because k is the same for each component, they are in-phase.

In the wave picture the circumference 2pr of an orbit of radius r must contain an integral number of wavelengths nl ¼ 2pr ð1:14Þ where n ¼ 1; 2; 3; . . ; 1, for a standing wave to be set up. 3(b) shows how a travelling wave results when n is not an integer: the wave interferes with itself and is destroyed. The picture of the electron in an orbit as a standing wave does, however, pose the important question of where the electron, regarded as a particle, is. We shall consider the answer to this for the case of an electron travelling with constant velocity in a direction x.

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Mathematics, Science and Epistemology, Philosophical Papers by Imre Lakatos

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