On the lifetime-width relation for a decaying state and the uncertainty principle

Key Points

• The aim is to present a new formulation of the uncertainty relation that connects lifetime and energy width of excited states.
• Developed a novel theoretical expression related to the uncertainty principle.
• Analyzed the implications of the new formulation regarding energy and time.
• Explored the relationship between the lifetime of excited states and their energy width.
• Established that the lifetime of excited states is related to their energy width through the derived expression.
• Showed that this connection is independent of the traditional uncertainty relation.
• Provided theoretical justification for the newly proposed relationship.