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Spatial vs momentum translation operators in quantum mechanics

In quantum mechanics, a translation operator allows one to rigidly shift the wavefunction by a certain amount. The translation could be in the spatial, momentum, or time domain, among others. The translation operator finds great utility in many topic related to quantum mechanics, such as the coherent states, symmetries, periodic systems, among many others. In this video, we discussed the spatial and momentum translation operation on the ket, bra and the wavefunctions, and end with a concrete example using the Gaussian wave packet. Technical Content: Tony Low Video Production: Katie Low, Tony Low