1. A and B are two operators, such that [A, B] = c, where c is...

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1. A and B are two operators, such that [A, B] = c, where c is a number. (a) Show that, e Be=B+c B] = = nc A(n-1). [Hint: First show that [A", Then show that [e4, B] = ceª. (b) Use the above result to show that eA А Bn e¯A = (B + c)" (c) Use the above result again to show that eª e³ e-A A B А е B = ece (d) The above result can be used to prove (You must show) e A e(A+B) e-A= eºe(A+B) А 1. A and B are two operators, such that [A, B] = c, where c is a number. (a) Show that, e Be=B+c B] = = nc A(n-1). [Hint: First show that [A", Then show that [e4, B] = ceª. (b) Use the above result to show that eA А Bn e¯A = (B + c)" (c) Use the above result again to show that eª e³ e-A A B А е B = ece (d) The above result can be used to prove (You must show) e A e(A+B) e-A= eºe(A+B) А

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