Bethe managed to perform the calculation on the train from New York to Schenectady, where he was working for General Electric. He did so by realising that it was a non-relativistic process, which greatly simplified the calculation. The bare energy was easily removed as it was already included in the observed mass of the electron. The self energy term now increased logarithmically instead of linearly, making it mathematically convergent. Bethe arrived at a value for the Lamb shift of 1040 MHz, extremely close to that obtained experimentally by Lamb and Retherford. His paper, published in the Physical Review in August 1947, was only three pages long and contained just twelve mathematical equations, but was enormously influential. It had been presumed that the infinities indicated that QED was fundamentally flawed, and that a new, radical theory was required; Bethe demonstrated that this was not necessary.