Yes you can, however it takes a decent amount of arm/wrist strength to take the the recoil from the round. You need to understand the term free recoil first, which is often misunderstood.
Free recoil is the kinetic energy transmitted to the shooter after firing a round. The amount of energy transmitted will vary from different caliber rounds. In this case we're talking about the Desert Eagle, and since this gun can be modified to hold several types of ammo, we'll stick to the standard 50AE bullet. This recoil is serious, You will need a bit of muscle and know how to position your body correctly in order to take the recoil. If you cannot control the recoil it will fly out of your hand, or possibly kick back into your face. In the best case scenario, the gun will jam as a result of not completing the action.
But to answer you question, Yes, you can fire a Desert Eagle with one hand with the proper training and technique. Although it is not as easy as the movies make it out to be.
As always, the best advice is training, and always gaining what knowledge you can from experienced shooters. Train hard, train often, and train safe.
I've also included some links to a few videos where you can actually see a professional shooting a Desert Eagle 50AE with one hand. You will see it can be done, but only if your an experienced shooter and know what to expect.
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