Quantum Physics | United States America (US)

Create: 2025-05-01 Update: 2025-06-30 03:28:05

مکانیک کوانتومی نسبیتی

معادله شرودینگر دینامیک ذرات غیرنسبیتی را توضیح می‌دهد. در این معادله مکان و زمان به صورت متقارن ظاهر نشده است. زمان به صورت مشتق اول و مکان به صورت مشتق دوم حضور دارد.
طبق نسبیت خاص، فضا و زمان باید متقارن باشند بنابراین برای نوشتن معادله نسبیتی باید یا مشتق زمان مرتبه دوم یا مشتق مکان مرتبه اول شود.
مسیر اول به معادله کلاین-گوردون منجر می‌شود. این معادله مشکلاتی دارد که پاسخ انرژی منفی یکی از آنهاست.
مسیر دوم به معادله دیراک ختم می‌شود. در این معادله نیز حل انرژی منفی وجود دارد. دیراک برای حل این مشکل، به دریای الکترونی متوسل شد. او گفت می‌توان چنین تصور کرد که حالتهای با انرژی منفی توسط دریایی از الکترون ها پر شده و طبق اصل طرد پاولی بقیه الکترون ها نمیتوانند در این حالتهای انرژی منفی سقوط کنند. یادآوری میکنم که طبق اصل طرد، هیچ دو فرمیونی نمیتوانند دقیقا در یک حالت کوانتومی قرار بگیرند.
معادله دیراک ذرات با اسپین 1/2 مانند الکترون را توصیف می‌کند و مشخص شد که معادله کلاین-گوردون مربوط به ذرات بدون اسپین است.
از طرفی شرط پایستگی ذرات که در مکانیک کوانتومی غیرنسبیتی وجود دارد، در کوانتوم نسبیتی وجود نخواهد داشت. زیرا ذرات می‌توانند خلق و نابود شوند. با چنین دیدگاهی، معادله دیراک و کلاین-گوردون معادلات میدان هستند که اعمال عملگر های خلق و فنا موجب تولید یا نابودی ذرات می‌شود. با چنین تفسیری از این معادلات مشکل انرژی منفی نیز حل می‌شود. هرچند برای یک ذره انرژی منفی معنا ندارد ولی برای میدان چنین مشکلی وجود ندارد.

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Quantum Physics

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مکانیک کوانتومی نسبیتی

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