ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ хуудасны эх кодыг харах

<nowiki><div style="max-height: 80vh; writing-mode: vertical-lr; font-family: 'Noto Sans Mongolian'"></nowiki>

ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠪᠣᠯ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠣᠢᠢᠯᠠᠭᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠤᠨ ᠨᠢᠭᠡ ᠶᠤᠮ᠃ ᠡᠨᠡᠬᠦᠦ ᠵᠠᠷᠴᠢᠮ ᠢᠢᠠᠷ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠬᠣᠣᠰ ᠹᠢᠽᠢᠻ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠨᠤᠭᠦᠳ ᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠨᠠᠷᠢᠨ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠵᠦ ᠦᠵᠡᠳᠡᠭ᠃ ᠨᠢᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠬᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠢᠯᠡᠭᠦᠦ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠨ᠎ᠡ᠂ ᠨᠥᠭᠦᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢᠨ ᠬᠡᠮᠵᠢᠯᠲᠡ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠪᠠᠭᠤᠷᠠᠨ᠎ᠠ᠃ ᠡᠨᠡ ᠪᠣᠯ ᠠᠯᠢᠪᠠ ᠢᠢ ᠳᠤᠷᠠ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠪᠠᠷ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ ᠰᠣᠩᠭᠤᠳᠠᠭ ᠹᠢᠽᠢᠻ ᠦᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠡᠴᠡ ᠻᠸᠠᠨ᠍ᠲ ᠹᠢᠽᠢᠻ ᠢᠯᠭᠠᠭᠳᠠᠬᠤ ᠭᠣᠣᠯ ᠣᠨᠴᠠᠯᠢᠭ ᠶᠤᠮ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠢ 1927 ᠣᠨ ᠳᠤ ᠭᠧᠷᠮᠠᠨ ᠤ ᠹᠢᠽᠢᠻᠴᠢ ᠸᠢᠷᠨᠢᠷ ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌Werner Heisenberg ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ᠃

<nowiki>__TOC__</nowiki>

<nowiki>=ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ=</nowiki>

ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠨ ᠬᠠᠮᠤᠭ ᠤᠨ ᠲᠦᠭᠡᠮᠡᠯ ᠵᠢᠱᠢᠶ᠎ᠡ ᠲᠠᠲᠤᠳᠠᠭ ᠬᠡᠪᠡᠷᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠤᠬᠠᠢ ᠳᠤ ᠶᠠᠷᠢᠭᠳᠠᠳᠠᠭ᠃ ᠡᠭᠦᠨ ᠦ ᠮᠠᠲ᠋ᠧᠮᠠᠲᠢᠻ ᠢᠯᠡᠷᠡᠬᠡᠢᠢᠯᠡᠯ ᠨᠢ:


Δ𝑥⋅Δ𝑝≥ℏ/2


ᠡ᠊ᠨᠳᠡ:


Δx ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃

Δp ᠨᠢ ᠢᠮᠫᠦ᠋ᠯᠰ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃

ℏ ᠨᠢ ᠪᠠᠭᠠ ᠫᠯᠠᠠᠨ᠍ᠻ ᠤᠨPlank ᠲᠣᠭᠲᠠᠮᠠᠯ (ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠲᠣᠭᠲᠠᠮᠠᠯ).

ᠡᠨᠡ ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠢᠰᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠨᠢ ᠶᠠᠮᠪᠠᠷ ᠨᠢᠭᠡ ᠲᠣᠭᠲᠠᠮᠠᠯ ᠤᠳᠬ᠎ᠠ ᠡᠴᠡ ᠢᠮᠠᠭᠲᠠ ᠶᠡᠬᠡ ᠪᠤᠶᠤ ᠲᠡᠩᠴᠠᠭᠦᠦ ᠪᠠᠢᠢᠬᠤ ᠶᠣᠰᠤᠲᠠᠢ ᠢᠢ ᠬᠠᠷᠠᠭᠤᠯᠵᠤ ᠪᠠᠢᠢᠭ᠎ᠠ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠬᠣᠶᠠᠷ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ ᠦ ᠤᠳᠬ᠎ᠠ ᠢᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠲᠡᠭᠦᠰ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯᠲᠠᠢ ᠮᠡᠳᠡᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ ᠶᠤᠮ᠃


<nowiki>=ᠵᠦᠢᠯᠴᠢᠯᠡᠪᠡᠰᠦ=</nowiki>

# '''ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ - ᠪᠥᠭᠡᠮᠯᠢᠭ ᠬᠣᠶᠠᠷᠳᠠᠮᠠᠯ ᠴᠢᠨᠠᠷ:''' ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠻ ᠲᠤ ᠡᠯᠧᠻᠲᠷᠣᠨ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠥᠭᠡᠮᠰ '''ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ ᠬᠢᠭᠡᠳ ᠪᠥᠭᠡᠮᠯᠢᠭ ᠴᠢᠨᠠᠷ ᠲᠠᠢ ᠪᠠᠢᠢᠳᠠᠭ᠃''' ᠪᠥᠭᠡᠮ ᠦᠨ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠭᠡᠵᠦ ᠦᠵᠡᠵᠦ ᠪᠣᠯᠬᠤ ᠪᠥᠭᠡᠳ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ ᠲᠠᠢ ᠬᠣᠯᠪᠤᠵᠤ ᠦᠵᠡᠳᠡᠭ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠪᠠᠯ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠣᠯᠬᠤ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠢ ᠨᠢ ᠴᠢᠨᠠᠳᠤ ᠲᠣᠭᠲᠤᠭᠠᠭᠰᠠᠨ ᠪᠥᠭᠡᠮ ᠦᠨ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ (ᠢᠮᠫᠦ᠋ᠯᠰ) ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠠᠢᠢᠳᠠᠭ ᠡᠴᠡ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠷᠭᠤᠨ ᠭᠠᠷᠴᠤ ᠪᠠᠢᠢᠨ᠎ᠠ᠃
# '''ᠵᠥᠪᠬᠡᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢᠢᠡᠷ ᠬᠢᠵᠠᠭᠠᠷᠯᠠᠭᠳᠠᠬᠤ ᠦᠭᠡᠢ''': ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠪᠠ ᠴᠠᠭ ᠬᠤᠭᠠᠴᠠᠭ᠎ᠠ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠤᠰᠤᠳ ᠬᠣᠣᠰ ᠬᠤᠪᠢᠰᠠᠭᠴᠢ ᠨᠤᠭᠤᠳ ᠲᠤ ᠪᠠᠰᠠ ᠢᠯᠡᠷᠡᠨ᠎ᠡ᠃ ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ᠂ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠡᠨᠧᠷᠭᠢ ᠪᠣᠯᠤᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠬᠡᠮᠵᠢᠭᠰᠡᠨ ᠴᠠᠭ ᠤᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠬᠠᠷᠢᠴᠠᠭ᠎ᠠ ᠦᠢᠯᠡᠴᠢᠯᠡᠳᠡᠭ᠌ :


ΔE⋅Δt≥ℏ2


ᠡᠨᠡ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠨᠡᠩ ᠪᠣᠭᠤᠨᠢ ᠬᠤᠭᠠᠴᠠᠭᠠᠨ ᠤ ᠬᠦᠷᠢᠶᠡᠨ ᠳᠦ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ᠂ ᠬᠠᠷᠢᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠪᠡᠯ ᠴᠠᠭ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠭᠲᠤᠭᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ᠃

# '''ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ''': ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠤᠨ ᠴᠢᠨᠠᠷ ᠪᠣᠯᠬᠤ ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ ᠤᠨ (non-determinism) ᠲᠤᠰᠬᠠᠯ ᠶᠤᠮ᠃ ᠰᠥᠩᠭᠤᠳᠠᠭ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠲᠤ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠪᠦᠬᠢ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠳᠦᠷᠰᠦᠯᠡᠳᠡᠭ ᠪᠣᠯ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠬᠤᠪᠢ᠋ ᠳᠤ ᠡᠨᠡ ᠨᠢ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠡᠭᠢ ᠠᠵᠡᠢ᠃ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲᠧᠮ ᠢ ᠵᠥᠪᠬᠡᠨ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠤᠳᠬ᠎ᠠ ᠪᠠᠷ ᠯᠠ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠳᠠᠭ᠃
# '''ᠤᠳᠬ᠎ᠠ ᠤᠴᠢᠷ ᠨᠢ''': ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠲᠠᠯᠠ ᠪᠠᠷ ᠬᠢ ᠻᠣᠫᠢᠨ᠍ᠾᠠᠭᠢᠨ ᠤ ᠲᠠᠢᠢᠯᠠᠪᠦᠷᠢ᠋ ᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠴᠢᠨᠠᠷ ᠨᠢ ᠪᠢᠳᠡᠨ ᠦ ᠬᠡᠮᠵᠢᠬᠦ ᠬᠡᠷᠡᠭᠰᠡᠯ ᠦᠨ ᠲᠡᠭᠦᠰ ᠪᠤᠰᠤ ᠡᠴᠡ ᠡᠭᠦᠳᠡᠯ ᠲᠡᠢ ᠪᠢᠰᠢ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠭᠠᠯᠢ ᠢᠢᠨ ᠰᠠᠭᠤᠷᠢ ᠰᠢᠨᠵᠢ ᠭᠡᠵᠦ ᠥᠬᠦᠯᠡᠳᠡᠭ᠃ ᠥᠭᠡᠷ᠎ᠡ ᠪᠤᠰᠤᠳ ᠲᠠᠢᠢᠯᠠᠪᠦᠤᠷᠢ ᠨᠤᠭᠤᠳ ᠡᠭᠦᠨ ᠲᠡᠢ ᠤᠭᠯᠠᠭᠤᠷᠭ᠎ᠠ ᠪᠠᠷ ᠢᠢᠠᠨ ᠨᠡᠢᠢᠴᠡᠬᠦ ᠪᠠ ᠦᠯᠦ ᠶᠠᠯᠢᠭ ᠢᠯᠭᠠᠭ᠎ᠠ ᠪᠤᠢ᠃


ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠠᠯᠢᠪᠠ ᠹᠢᠽᠢᠻ ᠰᠢᠰᠲᠧᠮ ᠢ ᠮᠠᠳᠠᠭ ᠦᠭᠡᠢ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ ᠭᠡᠳᠡᠭ ᠲᠦ ᠵᠤᠷᠰᠢᠭᠰᠠᠨ ᠪᠢᠳᠡᠨ ᠦ "ᠰᠣᠩᠭᠤᠳᠠᠭ" (classical) ᠬᠤᠷᠠᠨ ᠮᠡᠳᠡᠬᠦᠢ ᠢᠢ ᠡᠪᠳᠡᠵᠦ᠂ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠢᠢᠠᠷ ᠳᠦᠷᠰᠦᠯᠡᠭᠳᠡᠬᠦ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠴᠢᠨᠠᠷ ᠤᠨ ᠲᠣᠳᠤ ᠲᠣᠮᠤᠷᠠᠭᠤᠨ ᠢᠯᠡᠷᠡᠯ ᠪᠣᠯᠳᠠᠭ᠃