A jet engine is not the obvious way to power a locomotive. But, like most things, it has been done. Jet engines are inefficent at low speeds, and this was fully appreciated; they were tried out with high-speed passenger trains as a goal. The propulsive efficiency of any jet engine approaches its maximum of 100% when the forward speed approaches that of the exhaust gases. At one-tenth of this speed efficiency will be as low as 20%

THE NYC M-497 JET RDC (USA)

Left: The M-497 Black Beetle: 1966 The M-497 was a project of the New York Central Railroad. (NYCR) It was based on an existing Budd Rail Diesel Car, a type commonly used for short commuter trips, and for rural use where traffic was light. It was usually powered by a single diesel engine of 275 to 300 HP. It is not currently clear if the diesel engine was retained in the locomotive after the jets were fitted. As part of the conversion a streamlined front was fitted that was more than a bit ugly; hence it was called The Black Beetle. The jet locomotive made many successful high-speed runs, and on July 23, 1966, the M-497 achieved a speed of 183.7 mph, an American rail speed record still standing today. However the project was not developed further. There is a YouTube video of the M-497.

Railway speed records can get very complicated, depending on how you classify the locomotive and the track. There is a Wikipedia page on them.

The tracks that the NYC M-497 jet loco was tested on in 1966 are currently (2014) part of NORFOLK SOUTHERN.

Left: The J47 jet engine The jet engines on the top of the locomotive were surplus J-47-GE-15's which were used on the B-36 and the B-47 USAF bombers. It was the first axial-flow turbojet approved for commercial aircraft use in the USA. Note that the engine is long and thin compared with modern jet engines.

There is a Wikipedia page on jet locomotives.