Atomic Energy Levels: Discrete vs Continuous

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Atomic energy levels are discrete due to the eigenvalue spectrum of the Hamiltonian for hydrogen-like atoms, which results from the principles of quantum mechanics. Energy is emitted in quantized amounts, or quanta, rather than continuously. Understanding this concept requires a foundational knowledge of quantum mechanics. For further details, resources such as the Wikipedia page on hydrogen-like atoms provide comprehensive explanations. Mastery of these principles is essential for grasping atomic structure and behavior.
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Why in atom, ther r discrete energy level & not continous?
and energy emitted, from atom is in quata only?please give me exat answer or a related websites.
thanx in advance:redface:
 
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Exact answer: because the eigenvalue spectrum of the Hamiltonian for a Hydrogen-like atom is discrete. To understand this you need to learn basic quantum mechanics. Here is a summary of the exact solution to the hydrogen atom:

http://en.wikipedia.org/wiki/Hydrogen-like_atom
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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